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In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder's inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N and T = R ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011). [ABSTRACT FROM AUTHOR]

We completely characterize the boundedness of area operators from the Bergman spaces A α p (B n) to the Lebesgue spaces L q (S n) for all 0 < p,q < ∞. For the case n = 1, some partial results were previously obtained by Wu in [Wu, Z.: Volterra operator, area integral and Carleson measures, Sci. China Math., 54, 2487–2500 (2011)]. Especially, in the case q < p and q < s, we obtain some characterizations for the area operators to be bounded. We solve the cases left open there and extend the results to n-complex dimension. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain the boundedness of commutators of Hardy operators with rough kernels on grand variable Herz spaces K ˙ q ⁢ (⋅) a ⁢ (⋅) , u , θ ⁢ (ℝ n) by applying some properties of variable exponent. Moreover, by using the idea of grand variable Herz–Morrey spaces, we will prove the boundedness of Hardy operators on these spaces. [ABSTRACT FROM AUTHOR]

The purpose of this article is to present one and two-weight inequalities for bilinear multiplier operators in Dunkl setting with multiple Muckenhoupt weights. In order to do so, new results regarding Littlewood–Paley type theorems and weighted inequalities for multilinear Calderón–Zygmund operators in Dunkl setting are also proved. [ABSTRACT FROM AUTHOR]

In this paper, the authors characterize those φ, holomorphic self-maps of B, for which the composition operator $ C_{\varphi } $ C φ is bounded (or compact) on F(p,q,s) in some cases. Moreover, the following results are given. If 1

Let D be the unit disc in the complex plane. Given a positive finite Borel measure μ on the radius [0, 1), we denote the n-th moment of μ as μ n , that is, μ n = ∫ [ 0 , 1) t n d μ (t). The Cesàro-like operator C μ , s is defined on H (D) as follows: If f (z) = ∑ n = 0 ∞ a n z n ∈ H (D) then C μ , s (f) is defined by C μ , s (f) (z) = ∑ n = 0 ∞ μ n ∑ k = 0 n Γ (n - k + s) Γ (s) (n - k) ! a k z n , z ∈ D. In this paper, our focus is on the action of the C e s a ` r o -type operator C μ , s on spaces of analytic functions in D . We characterize the boundedness (compactness) of the C e s a ` r o -like operator C μ , s , acting between the Bloch space B and the Bergman space A p . [ABSTRACT FROM AUTHOR]

Let $ 0 \lt p \lt \infty $ 0 < p < ∞ and $ K:[0,\infty)\to [0,\infty) $ K : [ 0 , ∞) → [ 0 , ∞) be a nondecreasing and right-continuous function. A new Dirichlet-Morrey type space $ \mathcal {D}^{p,K}_{p-1} $ D p − 1 p , K is introduced in this paper. The boundedness of the identity operator $ I_d $ I d from $ \mathcal {D}^{p,K}_{p-1} $ D p − 1 p , K to tent spaces $ \mathcal {T}_{K}^{p}(\mu) $ T K p (μ) is characterized. As an application, the boundedness, compactness and essential norm of Volterra integral operators on $ \mathcal {D}^{p,K}_{p-1} $ D p − 1 p , K are investigated. [ABSTRACT FROM AUTHOR]

In this article, we analyze the boundedness for the fractional bilinear Hardy operators on variable exponent weighted Morrey–Herz spaces M K ˙ q , p (⋅) α (⋅) , λ (w) . Similar estimates are obtained for their commutators when the symbol functions belong to BMO space with variable exponents. [ABSTRACT FROM AUTHOR]

Let ω be a doubling weight and 0 < p ≤ q < ∞ {0

Let L = - Δ ℍ n + V {L=-{\Delta}_{\mathbb{H}^{n}}+V} be a Schrödinger operator on Heisenberg groups ℍ n {\mathbb{H}^{n}} , where Δ ℍ n {{\Delta}_{\mathbb{H}^{n}}} is the sub-Laplacian, the nonnegative potential V belongs to the reverse Hölder class B 풬 / 2 {B_{\mathcal{Q}/2}} . Here 풬 {\mathcal{Q}} is the homogeneous dimension of ℍ n {\mathbb{H}^{n}} . In this article, we introduce the fractional heat semigroups { e - t ⁢ L α } t > 0 {\{e^{-tL^{\alpha}}\}_{t>0}} , α > 0 {\alpha>0} , associated with L. By the fundamental solution of the heat equation, we estimate the gradient and the time-fractional derivatives of the fractional heat kernel K α , t L ⁢ ( ⋅ , ⋅ ) {K_{\alpha,t}^{L}(\,\cdot\,,\cdot\,)} , respectively. As an application, we characterize the space BMO L γ ⁢ ( ℍ n ) {\mathrm{BMO}_{L}^{\gamma}(\mathbb{H}^{n})} via { e - t ⁢ L α } t > 0 {\{e^{-tL^{\alpha}}\}_{t>0}} . [ABSTRACT FROM AUTHOR]

In this paper, we study the boundedness of p-adic Riesz potential on two-weighted Morrey–Herz spaces with both power weight and Muckenhoupt weight. Moreover, the boundedness for commutators of p-adic Riesz potential with symbols in Lipschitz spaces and weighted central BMO spaces on such spaces are also established. [ABSTRACT FROM AUTHOR]

It is known, by Gelfand theory, that every commutative JB $ ^* $ ∗ -triple admits a representation as a space of continuous functions of the form \[ C_0^{\mathbb{T}}(L) = \{ a\in C_0(L) : a(\lambda t) = \lambda a(t), \ \forall \lambda\in \mathbb{T}, t\in L\}, \] C 0 T (L) = { a ∈ C 0 (L) : a (λ t) = λ a (t) , ∀ λ ∈ T , t ∈ L } , where L is a principal $ \mathbb {T} $ T -bundle and $ \mathbb {T} $ T denotes the unit circle in $ \mathbb {C}. $ C. We provide a full technical description of all orthogonality preserving (non-necessarily continuous nor bijective) linear maps between commutative JB $ ^* $ ∗ -triples. Among the consequences of this representation, we obtain that every linear bijection preserving orthogonality between commutative JB $ ^* $ ∗ -triples is automatically continuous and bi-orthogonality preserving. [ABSTRACT FROM AUTHOR]

We find sufficient conditions for a self-map of the unit ball to converge uniformly under iteration to a fixed point or idempotent on the entire ball. Using these tools, we establish spectral containments for weighted composition operators on Hardy and Bergman spaces of the ball. When the compositional symbol is in the Schur–Agler class, we establish the spectral radii of these weighted composition operators. [ABSTRACT FROM AUTHOR]

Let (σ , V (1) , ⋯ , V (k)) be a pure doubly commuting isometric representation of the product system E on a Hilbert space H V. A σ -invariant subspace K is said to be Beurling quotient subspace of H V if there exist a Hilbert space H W , a pure doubly commuting isometric representation (π , W (1) , ⋯ , W (k)) of E on H W and an isometric multi-analytic operator M Θ : H W → H V , such that K = H V ⊖ M Θ H W , where Θ : W H W → H V is an inner operator and W H W is the generating wandering subspace for (π , W (1) , ⋯ , W (k)). In this article, we prove the following characterization of the Beurling quotient subspaces: A subspace K of H V is a Beurling quotient subspace if and only if (I E j ⊗ ((I E i ⊗ P K) - T ~ (i) ∗ T ~ (i))) (t i , j ⊗ I H V) (I E i ⊗ ((I E j ⊗ P K) - T ~ (j) ∗ T ~ (j))) = 0 , where T ~ (i) : = P K V ~ (i) (I E i ⊗ P K) and 1 ≤ i , j ≤ k. As a consequence, we derive a concrete regular dilation theorem for a pure, completely contractive covariant representation (σ , V (1) , ⋯ , V (k)) of E on a Hilbert space H V which satisfies Brehmer–Solel condition and using it and the above characterization, we provide a necessary and sufficient condition that when a completely contractive covariant representation is unitarily equivalent to the compression of the induced representation on the Beurling quotient subspace. Further, we study the relation between Sz. Nagy–Foias-type factorization of isometric multi-analytic operators and joint invariant subspaces of the compression of the induced representation on the Beurling quotient subspace. [ABSTRACT FROM AUTHOR]

In the present paper, convergence in modular spaces is investigated for a class of nonlinear discrete operators, namely the nonlinear multivariate sampling Kantorovich operators. The convergence results in the Musielak-Orlicz spaces, in the weighted Orlicz spaces, and in the Orlicz spaces follow as particular cases. Even more, spaces of functions equipped by modulars without an integral representation are presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the frequent hypercyclicity of a scalar multiple of the tensor product of two linear fractional composition operators λ C φ ⊗ C ψ on S ν ⊗ S ν , where S ν is the weighted Dirichlet space. We will restrict the discussion to the situations that both φ and ψ are hyperbolic non automorphisms, hyperbolic automorphisms and parabolic automorphisms, respectively. Meanwhile, we give the equivalent conditions of λ C φ ⊗ C ψ to be frequently hypercyclic, hypercyclic, mixing and chaotic. [ABSTRACT FROM AUTHOR]

In this paper, we characterize bounded, compact, and order bounded sums of weighted composition-differentiation operators from Bergman-type spaces to weighted Banach spaces of analytic functions. [ABSTRACT FROM AUTHOR]

Recent advances in machine learning have highlighted the importance of using group equivariant non-expansive operators for building neural networks in a more transparent and interpretable way. An operator is called equivariant with respect to a group if the action of the group commutes with the operator. Group equivariant non-expansive operators can be seen as multi-level components that can be joined and connected in order to form neural networks by applying the operations of chaining, convex combination and direct product. In this paper we prove that each linear G-equivariant non-expansive operator (GENEO) can be produced by a weighted summation associated with a suitable permutant measure, provided that the group G transitively acts on a finite signal domain. This result is based on the Birkhoff–von Neumann decomposition of doubly stochastic matrices and some well known facts in group theory. Our theorem makes available a new method to build all linear GENEOs with respect to a transitively acting group in the finite setting. This work is part of the research devoted to develop a good mathematical theory of GENEOs, seen as relevant components in machine learning. [ABSTRACT FROM AUTHOR]

We study the weighted Bergman spaces on finitely connected planar domains. They are isomorphic to the product of weighted Bergman spaces on the unit disk. Using this, we characterize the Carleson embeddings and prove kernel estimates. We characterize bounded, compact and Schatten class composition and Toeplitz operators on these spaces. Our results generalize several recent ones in the unit disk or simply connected case. [ABSTRACT FROM AUTHOR]

Necessary and sufficient conditions for the boundedness of multilinear Hausdorff operators on local Morrey-type spaces are obtained and sharp constants are also given. As applications, we generalize our results to some concrete operators derived from Hausdorff operators, such as the Hardy operator and its dual operator, the weighted Hardy–Littlewood average, among others. [ABSTRACT FROM AUTHOR]

We utilize the ( A α p , q ) -Carleson measure to investigate the bounded small Hankel operator h f α acting between the Bergman-type space A α p and A α q ¯ on the complex unit ball B n for some α ≤ − 1 . For n ≥ 2 , and f ∈ H ( B n ) , we have the conclusions: Suppose α ≤ − 1 , max { 1 , − 2 α − 2 } < p < ∞ and p N + α > − 1 . Then h f α : A α p → A α p ¯ is bounded if and only if | R N f ( z ) | p d v p N + α ( z ) is an ( A α p , p ) -Carleson measure. Suppose − n − 1 < α ≤ − 1 , max { 1 , − 2 α − 2 } < p < q < ∞ and p N > max { q − p p ( n + 1 + α ) − 2 ( α + 1 ) , − p ( α + 1 ) p − 1 } . Then h f α : A α p → A α q ¯ is bounded if and only if | R N f ( z ) | q d v q N + α ( z ) is an ( A α p , q ) -Carleson measure. Suppose 1 < q < p < ∞ , α ≤ − 1 , N be a positive integer such that q N + α > − 1 . If | R N f ( z ) | q d v q N + α ( z ) is an ( A α p , q ) -Carleson measure, then h f α : A α p → A α q ¯ is bounded. Let κ = p q p − q and κ ′ = κ κ − 1 . If α + ( p − 1 ) κ ′ N > − 1 and h f α : A α p → A α q ¯ is bounded, then f ∈ A α κ with ‖ f ‖ A α κ ≲ ‖ h f α ‖ . If | R N f ( z ) | q d v q N + α ( z ) is an ( A α p , q ) -Carleson measure, then f ∈ A α κ . But, there is an f ∈ A α κ such that | R N f ( z ) | q d v q N + α ( z ) is not an ( A α p , q ) -Carleson measure. Suppose α ≤ − 1 , max { 1 , − 2 α − 2 } < p < ∞ and p N + α > − 1 . Then h f α : A α p → A α p ¯ is bounded if and only if | R N f ( z ) | p d v p N + α ( z ) is an ( A α p , p ) -Carleson measure.Suppose − n − 1 < α ≤ − 1 , max { 1 , − 2 α − 2 } < p < q < ∞ and p N > max { q − p p ( n + 1 + α ) − 2 ( α + 1 ) , − p ( α + 1 ) p − 1 } . Then h f α : A α p → A α q ¯ is bounded if and only if | R N f ( z ) | q d v q N + α ( z ) is an ( A α p , q ) -Carleson measure.Suppose 1 < q < p < ∞ , α ≤ − 1 , N be a positive integer such that q N + α > − 1 . If | R N f ( z ) | q d v q N + α ( z ) is an ( A α p , q ) -Carleson measure, then h f α : A α p → A α q ¯ is bounded. Let κ = p q p − q and κ ′ = κ κ − 1 . If α + ( p − 1 ) κ ′ N > − 1 and h f α : A α p → A α q ¯ is bounded, then f ∈ A α κ with ‖ f ‖ A α κ ≲ ‖ h f α ‖ . If | R N f ( z ) | q d v q N + α ( z ) is an ( A α p , q ) -Carleson measure, then f ∈ A α κ . But, there is an f ∈ A α κ such that | R N f ( z ) | q d v q N + α ( z ) is not an ( A α p , q ) -Carleson measure. If | R N f ( z ) | q d v q N + α ( z ) is an ( A α p , q ) -Carleson measure, then h f α : A α p → A α q ¯ is bounded.Let κ = p q p − q and κ ′ = κ κ − 1 . If α + ( p − 1 ) κ ′ N > − 1 and h f α : A α p → A α q ¯ is bounded, then f ∈ A α κ with ‖ f ‖ A α κ ≲ ‖ h f α ‖ .If | R N f ( z ) | q d v q N + α ( z ) is an ( A α p , q ) -Carleson measure, then f ∈ A α κ . But, there is an f ∈ A α κ such that | R N f ( z ) | q d v q N + α ( z ) is not an ( A α p , q ) -Carleson measure. [ABSTRACT FROM AUTHOR]

Inspired by natural classes of examples, we define generalized directed semi-trees and construct weighted shifts on them. Given an n-tuple of generalized directed semi-trees with certain properties, we associate an n-tuple of multiplication operators on a Hilbert space H 2 (β) of formal power series. Under certain conditions, H 2 (β) turns out to be a reproducing kernel Hilbert space consisting of holomorphic functions on some domain in C n and the n-tuple of multiplication operators on H 2 (β) is unitarily equivalent to an n-tuple of weighted shifts on generalized directed semi-trees. Finally, we exhibit two classes of examples of n-tuples of operators, which can be intrinsically identified as weighted shifts on generalized directed semi-trees. [ABSTRACT FROM AUTHOR]

Let Π = { z ∈ C / ℑ z > 0 } , the upper half-plane in the complex plane C . Let H (Π) be the set of all analytic functions on Π and S (Π) be the set of all analytic self-maps on Π. For φ ∈ S (Π) , N ∈ N 0 = N ∪ { 0 } and ψ (N) = (ψ 0 , ψ 1 , ... , ψ N) , where ψ j ∈ H (Π) , j = 0 , 1 , ... , N , define an operator T ψ (N) , φ (f) := ∑ j = 0 N ψ j ⋅ (f (j) ∘ φ) , f ∈ H (Π). In this paper, we characterize the boundedness and compactness of the operator T ψ (N) , φ on the Hardy, weighted-Bergman spaces on Π to weighted-type spaces on Π. [ABSTRACT FROM AUTHOR]

For 1 < p < ∞ and a nondecreasing function K on [ 0 , ∞ ) , we give an explicit derivative-free characterization of Q K type space, denoted by Q K p and characterize the boundary version of Q K p . By using these results, we prove the corona theorems both for Q K p ∩ H ∞ and for the multiplier algebra of Q K p under some assumptions of the weight function K. [ABSTRACT FROM AUTHOR]

The limit q-Lupaş operator emerged in the study of the Lupaş q-analogue of the Bernstein operator. Afterward, it has been found that it is connected to numerical analysis, computer aided geometric design, probability theory and other areas. In this paper, properties of block functions generating the limit q-Lupaş operator have been investigated. [ABSTRACT FROM AUTHOR]

We show that under an arithmetic condition the spectrum of a bounded multidimensional discrete Hausdorff operator in the Lebesgue space is an annulus (or a disc) centered at the origin, provided the perturbation matrices commute and are either positive or negative definite. Conditions for a point spectrum of such an operator to be empty are given and its norm is computed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a class of linear operators defined on a separable Hilbert space H . More precisely, we define the generalized Fourier multipliers T σ A : H → H , where σ are symbols which belong to L p (Z) , 1 ≤ p ≤ ∞ and A : H → H is a bounded linear operator which satisfies some suitable conditions. Moreover, we also define function of generalized Fourier multipliers F T σ A : H → H where F : C → C is a continuous function. We give some boundedness and compactness results and we also study Schatten-von Neumann properties for these classes of linear operators mentioned above. Further, we study the existence and the regularity of the solutions of the linear equations F T σ A f + λ f = g , f , g ∈ H , where F : R → R + is a real-valued non-negative continuous function and λ is a real positive number. At last, an example of function of generalized Fourier multipliers in connection to Weyl transform is given. [ABSTRACT FROM AUTHOR]

In this paper, we consider the weighted Hardy space H p (ω) induced by an A p weight ω. We characterize the positive Borel measures μ such that the identity operator I d : H p (ω) → L q (d μ) is bounded when 1 ≤ p , q < ∞. As an application, we obtain necessary and sufficient conditions for the boundedness of the generalized area operator A μ , ν from H p (ω) to L q (ω). [ABSTRACT FROM AUTHOR]

In this paper, we characterize those positive Borel measurable symbols μ on C n that induce the Toeplitz operators T μ α to be bounded or compact between different Fock–Sobolev–type spaces F α p and F α ∞ with 0 < p ≤ ∞ . [ABSTRACT FROM AUTHOR]

In this work, by the introduction of some parameters, a new half-discrete kernel function in the whole plane is defined, which involves both the homogeneous and the nonhomogeneous cases. By employing some techniques of real analysis, especially the method of a weight function, a new half-discrete Hilbert-type inequality with the new kernel function, as well as its equivalent Hardy-type inequalities are established. Moreover, it is proved that the constant factors of the newly obtained inequalities are the best possible. Finally, assigning special values to the parameters, some new half-discrete Hilbert-type inequalities with special kernels are presented at the end of the paper. [ABSTRACT FROM AUTHOR]

In this article, we mainly study the weighted composition-differentiation operator on the weighted Bergman space A α 2 and the derivative Hardy space S 1 2 , which characterize complex symmetric weighted composition-differentiation operator D u , φ . Moreover, the normality and self-adjointness of D u , φ are also discussed. [ABSTRACT FROM AUTHOR]

Let be a bounded symmetric domain realized as the unit open ball of JB*-triples. The authors will characterize the bounded weighted composition operator from the Bloch space to weighted Hardy space in terms of Kobayashi distance. The authors also give a sufficient condition for the compactness, and also give the upper bound of its essential norm. As a corollary, they show that the boundedness and compactness are equivalent for composition operator from to , when E is a finite dimension JB*-triple. Finally, they show the boundedness and compactness of weighted composition operators from to are equivalent when E is a finite dimension JB*-triple. [ABSTRACT FROM AUTHOR]

We prove the boundedness of the non-local operator L a u (x) = ∫ R d u (x + y) - u (x) - χ α (y) (∇ u (x) , y) a (x , y) dy | y | d + α from H p , w α (R d) to L p , w (R d) for the whole range of p ∈ (1 , ∞) , where w is a Muckenhoupt weight. The coefficient a(x, y) is bounded, merely measurable in y, and Hölder continuous in x with an arbitrarily small exponent. We extend the previous results by removing the largeness assumption on p as well as considering weighted spaces with Muckenhoupt weights. Using the boundedness result, we prove the unique solvability in L p spaces of the corresponding parabolic and elliptic non-local equations. [ABSTRACT FROM AUTHOR]

For any 1 ≤ p ≤ ∞, let Sp() be the space of holomorphic functions f on such that f′ belongs to the Hardy space Hp(), with the norm ∥f∥∑ = ||f||∞ +||f′||p. We prove that every approximate local isometry of Sp() is a surjective isometry and that every approximate 2-local isometry of Sp () is a surjective linear isometry. As a consequence, we deduce that the sets of isometric reflections and generalized bi-circular projections on Sp() are also topologically reflexive and 2-topologically reflexive. [ABSTRACT FROM AUTHOR]

Let L = - Δ H n + V be a Schrödinger operator on Heisenberg groups H n , where Δ H n is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class B q , q ≥ Q / 2 and Q = 2 n + 2 is the homogeneous dimension of H n . We establish a T1 criterion for the boundedness of γ -Schrödinger–Calderón–Zygmund operators on Campanato type spaces BMO L α (H n) . As an application, by the aid of regularity estimate for fractional heat semigroup { e - t L β } t > 0 , we prove the BMO L α -boundedness of operators generated by fractional heat semigroups including the maximal operators, the square functions, the Laplace transform type multipliers and the fractional integral associated with Schrödinger operator L via T1 theorem, respectively. [ABSTRACT FROM AUTHOR]

We study the compact intertwining relations for the multiplication operators between Hardy spaces and Bergman spaces in the unit ball of C n. [ABSTRACT FROM AUTHOR]

Quaternionic Fock space is a useful generalization of the Fock space in the complex plane, which plays an important role in quantum mechanics. In view of quaternionic operator theory this topic attains more diversity and complexity. In this paper we first explore the connection between the properties and about the difference of quaternionic weighted composition operators acting on slice regular Fock space with the function theoretic properties of the symbols. It can further imply some topological information on the set of quaternionic weighted composition operators. [ABSTRACT FROM AUTHOR]

In a self contained presentation we study the boundedness of the Laplace transform on the rearrangement invariant Lebesgue Lp-space, we use real analysis techniques provided by convex analysis and the K-method. [ABSTRACT FROM AUTHOR]

Starting from the well-known work of Cooper and Waldron published in 2000, the eigenstructure of various Bernstein-type operators has been investigated by many researchers. In this work, the eigenvalues and eigenvectors of the modified Bernstein operators Qn have been studied. These operators were introduced by S. N. Bernstein himself, in 1932, for the purpose of accelerating the approximation rate for smooth functions. Here, the explicit formulae for the eigenvalues and corresponding eigenpolynomials together with their limiting behavior are established. The results show that although some outcomes are similar to those for the Bernstein operators, there are essentially different ones as well. [ABSTRACT FROM AUTHOR]

In recent years, using the idea of analytic and bi-univalent functions, many ideas have been developed by different well-known authors, but the using Gegenbauer polynomials along with certain bi-univalent functions is very rare in the literature. We are essentially motivated by this recent research going on, here in our present investigation, we make use of certain q-derivative operator and Gegenbauer polynomials and define a new subclass of analytic and bi-univalent functions. We then obtain certain coefficient bounds, the Fekete–Szegö inequalities and upper bounds for the second-order Hankel determinant for the defined functions class. [ABSTRACT FROM AUTHOR]

In this paper, the authors characterize those φ, holomorphic self-maps of B, for which the composition operator C φ is bounded (or compact) on F(p,q,s) in some cases. Moreover, the following results are given. If 1<p<q + n + 1 and C φ satisfies some boundedness conditions, then C φ is compact on F(p,q,s) if and only if lim | z | → 1 − 1 − | z | 2 1 − | φ ( z ) | 2 = 0. If 1 ≤ p < ∞ and q + n + 1 < p < ∞ , then C φ is a compact operator on F(p,q,s) if and only if ‖ φ ‖ ∞ < 1 and φ l ∈ F ( p , q , s ) for all l ∈ { 1 , 2 , … , n } . If 1<p<q + n + 1 and C φ satisfies some boundedness conditions, then C φ is compact on F(p,q,s) if and only if lim | z | → 1 − 1 − | z | 2 1 − | φ ( z ) | 2 = 0. If 1 ≤ p < ∞ and q + n + 1 < p < ∞ , then C φ is a compact operator on F(p,q,s) if and only if ‖ φ ‖ ∞ < 1 and φ l ∈ F ( p , q , s ) for all l ∈ { 1 , 2 , … , n } . [ABSTRACT FROM AUTHOR]

In this paper, we are interested in operators arising from the product of a weighted composition operator and a maximal differential operator on the Fock space. Let T max and C u , φ denote a maximal differential operator and a weighted composition operator, respectively. We characterize some C -selfadjoint operators C u , φ T max with respect to special conjugations C . Moreover, we obtain a partial characterization of hermitian operator C φ T max . [ABSTRACT FROM AUTHOR]

Let μ be a normal function on [ 0 , 1) and p>0. Suppose φ is a holomorphic self-map on the unit ball B of C n . In this paper, the authors characterize the conditions such that the composition operator C φ is bounded or compact from the normal weight Dirichlet type space D μ p (B) to the normal weight Bloch type space B ν p (B) when n>1, where ν p (r) = (1 − r 2 ) n p μ 1 p (r) ( 0 ≤ r < 1). Moreover, the authors give a simple sufficient and necessary condition such that C φ is compact from D μ p (B) to B ν p (B) for some special cases. [ABSTRACT FROM AUTHOR]

In this paper, we study Hankel operators on the doubling Fock spaces for all possible 1 ≤ p , q < ∞ . We characterize those symbols f for which the Hankel operators H f and H f ¯ are simultaneously bounded or compact from doubling Fock space F φ p to Lebesgue space L φ q , where φ is a nonzero subharmonic function such that Δ φ d A is a doubling measure. [ABSTRACT FROM AUTHOR]

Let 0 < p < ∞ and K : [ 0 , ∞ ) → [ 0 , ∞ ) be a nondecreasing and right-continuous function. A new Dirichlet-Morrey type space D p − 1 p , K is introduced in this paper. The boundedness of the identity operator I d from D p − 1 p , K to tent spaces T K p ( μ ) is characterized. As an application, the boundedness, compactness and essential norm of Volterra integral operators on D p − 1 p , K are investigated. [ABSTRACT FROM AUTHOR]

Let L = - Δ + V be a Schrödinger operator with the potential V belonging to the reverse Hölder class B q , q > n / 2 . Denote by CMO θ (ρ) the vanishing mean oscillation type space associated with L. By the aid of the regularity estimates of the fractional heat kernel related with L, we investigate the weighted boundedness and compactness of the commutators of operators generated by fractional heat semigroups related to L and functions belonging to CMO θ (ρ) . [ABSTRACT FROM AUTHOR]

Let X be a completely regular Hausdorff space and E be a Banach space. Let Cb(X, E) (resp.) be the space of all bounded continuous (resp. bounded strongly Borel-measurable) functions f : X → E, equipped with the natural mixed topologies. Then whenever X or E is separable. We study the problem of extension of different classes of continuous linear operators acting from Cb(X, E) to a Banach space F to corresponding continuous linear operators acting from to F. [ABSTRACT FROM AUTHOR]

Approximation of a multivariate function is an important theme in the field of numerical analysis and its applications, which continues to receive a constant attention. In this paper, we provide a parameterized family of self-referential (fractal) approximants for a given multivariate smooth function defined on an axis-aligned hyper-rectangle. Each element of this class preserves the smoothness of the original function and interpolates the original function at a prefixed gridded data set. As an application of this construction, we deduce a fractal methodology to approach a multivariate Hermite interpolation problem. This part of our paper extends the classical bivariate Hermite's interpolation formula by Ahlin (Math. Comp. 18:264–273, 1964) in a twofold sense: (i) records, in particular, a multivariate generalization of this bivariate interpolation theory; (ii) replaces the unicity of the Hermite interpolant with a parameterized family of self-referential Hermite interpolants which contains the multivariate analogue of Ahlin's interpolant as a particular case. Some related aspects including the approximation by multivariate self-referential functions preserving Popoviciu convexity are given, too. [ABSTRACT FROM AUTHOR]

Let p > 0 and ν be a normal function on [0, 1). In this paper, several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D ν p (D) in the unit disc. [ABSTRACT FROM AUTHOR]

We characterize the Lvp(Rn)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${L^{p}_{v}}(\mathbb {R}^{n})$$\end{document}-Luq(Rn)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${L^{q}_{u}}(\mathbb {R}^{n})$$\end{document} boundedness of the Dunkl-Hausdorff operator for radially decreasing functions. Both the cases 1