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For $0, the Dirichlet–Morrey space $\mathcal {D}_p^{\lambda } $ is the space of all analytic function on the unit disc such that the measure $ |f'(z)|^2(1-|z|^2)^pdA(z)$ is a $p\lambda $ -Carleson measure. In this paper, we show that the corona theorem and the Wolff theorem hold for the multiplier algebra of Dirichlet–Morrey spaces.

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.

In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.

In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex ...

We study the boundedness and compactness of the generalized Volterra integral operator on weighted Bergman spaces with doubling weights on the unit disk. A generalized Toeplitz operator is defined and the boundedness, compactness and Schatten class of this operator are investigated on the Hilbert weighted Bergman space. As an application, Schatten class membership of generalized Volterra integral operators are also characterized. Finally, we also get the characterizations of Schatten class membership of generalized Toeplitz operator and generalized Volterra integral operators on the Hardy space $H^2$.

In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong...

In this paper, we study the boundedness and compactness of the inclusion mapping from Besov spaces to tent spaces. Meanwhile, the boundedness, compactness, and essential norm of Volterra integral operators from Besov spaces to general function spaces are also investigated.

In this paper, we study the boundedness and compactness of the Volterra integral operators from Dirichlet type spaces $${\mathcal {D}}^p_{p-2+s}$$ into Hardy spaces $${\mathcal {H}}^q$$ when $$1

The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.

A class of Dirichlet-Morrey spaces $ D_{\beta, \lambda} $ is introduced in this paper. For any positive Borel measure $ \mu $, the boundedness and compactness of the identity operator from $ D_{\beta, \lambda} $ into the tent space $ \mathcal{T}_s^1(\mu) $ are characterized. As an application, the boundedness of the Volterra integral operator $ T_g: D_{\beta, \lambda} \to F(1, \beta-s, s) $ is studied. Moreover, the essential norm and the compactness of the operator $ T_g $ are also investigated.

In this paper, some characterizations for the compact difference of composition operators on weighted Bergman spaces $$A^p_\omega $$ with doubling weights are given, which extend Moorhouse’s characterization for the difference of composition operators on the weighted Bergman space $$A^2_\alpha $$ .

The purpose of this paper is to study several different properties of the holomorphic $${\cal N}\left( {p,q,s} \right)$$ -type functions in the unit ball $$\mathbb{B}$$ of ℂn via Carleson measure techniques. More precisely, we establish an atomic decomposition on such spaces and then we solve the Gleason’s problem on them. We also study the distance problems between Bergman-type spaces $${A^{ - {q \over p}}}\left(\mathbb{R} \right)$$ and $${\cal N}\left( {p,q,s} \right)$$ -type spaces. These results yield some new characterizations of the holomorphic F(p, q, t)-functions.

This paper attempts to focus on the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm which combines the hybrid projection method and the inertial technique. The strong convergence theorems of this algorithm are obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of operator norms. Some numerical experiments in infinite Hilbert space are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existin

In this paper, some characterizations are given in terms of the boundary value and Poisson extension for the Dirichlet-type space D μ . The multipliers of D μ and Hankel-type operators from D μ to L 2 P μ d A are also investigated.

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi $ on Bergman type spaces $A_\omega ^p $ induced by a doubling weight ω. Let $X=\{u\in H(\mathbb{D} ): uC_\varphi \colon A_\omega ^p\to A_\omega ^p\ \text {is bounded}\}$. For some regular weights ω, we obtain that $X=H^\infty $ if and only if ϕ is a finite Blaschke product.

Some new characterizations for the boundedness and compactness of the difference of two weighted composition operators acting from $$H^\infty $$ to the Bloch space are given in this paper.

In this work, the boundedness and essential norm of weighted composition operators from the Zygmund space to nth weighted-type spaces are characterized. As a corollary, some characterizations for t...

In this paper, we study the boundedness and compactness of the identity operator $$I:BMOA_{\log }\rightarrow \mathcal {T}^{\infty }_{\log }(\mu )$$. As applications, we characterize the boundedness and compactness of the Volterra integral operators $$T_g$$ and $$I_g$$ on the space $$BMOA_{\log }$$. The estimations for the essential norm of $$T_g$$ and $$I_g$$ on the space $$BMOA_{\log }$$ are also given.

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on mappings. Finally, some numerical examples are presented to illustrate the results in this paper., 18 pages, 2 figures

With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms are guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.

This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.

In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.

The purpose of this paper is to study a new class of function spaces, called 𝒩 ⁢ ( p , q , s ) {\mathcal{N}(p,q,s)} -type spaces, in the unit ball 𝔹 {{\mathbb{B}}} of ℂ n {{\mathbb{C}}^{n}} . The Carleson measure on such spaces is investigated. Some embedding theorems among 𝒩 ⁢ ( p , q , s ) {\mathcal{N}(p,q,s)} -type spaces, weighted Bergman spaces and weighted Hardy spaces are established. As for applications, the Hadamard products and random power series on 𝒩 ⁢ ( p , q , s ) {\mathcal{N}(p,q,s)} -type spaces are also studied.

The purpose of this paper is to study a new class of function spaces, called N(p,q,s)-type spaces, in the unit ball B of Cn. We establish some basic properties of this new function space, together ...

In this paper, we give some estimates for the essential norm of weighted composition operators from analytic Besov spaces into Zygmund type spaces. In particular, a new characterization for the boundedness and compactness of the weighted composition operators uCϕ is obtained.

Let $$\lambda _i (i=1,\ldots ,k)$$ be nonzero complex scalars and $$\varphi _i (i=1,..,k)$$ be analytic self-maps of the unit disk $$\mathbb {D}$$ . We show that the operator $$\sum _{i=1}^k\lambda _iC_{\varphi _i}$$ is compact on the Bloch space $$\mathcal {B}$$ if and only if $$\begin{aligned} \lim _{n\rightarrow \infty }\Vert \lambda _1\varphi _1^n+\lambda _2\varphi _2^n+\cdots +\lambda _k\varphi _k^n\Vert _{\mathcal {B}}=0. \end{aligned}$$ We also study the linear combination of composition operators on the Banach algebra of bounded analytic functions.

In this paper, we study 2-complex symmetric composition operators with the conjugation $J$ on the Hardy space $H^2$. More precisely, we obtain the necessary and sufficient condition for the composition operator $C_\phi$ to be 2-complex symmetric when the symbols $\phi$ is an automorphism of $\mathbb D$. We also characterize the 2-complex symmetric composition operator $C_\phi$ on the Hardy space $H^2$ when $\phi$ is a linear fractional self-map of $\mathbb D$., Comment: 13 pages

In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. As well as, the iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.

In this paper, we prove the Mohebi-Radjabalipour Conjecture under an additional condition, and obtain a new invariant subspace theorem for subdecomposable operators. Our main results contain known results in the literature as special cases. Moreover, we give some specific examples to illustrate that the conditions in our theorem are significantly weaker, simpler and more nature than those in the known results.

In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.

In this paper, we introduce two new modified inertial Mann Halpern and viscosity algorithms for solving fixed point problems. We establish strong convergence theorems under some suitable conditions. Finally, our algorithms are applied to split feasibility problem, convex feasibility problem and location theory. The algorithms and results presented in this paper can summarize and improve corresponding results previously known in this area., 11 pages, 4 Figures

In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for our algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performances of the proposed algorithms and provide a comparison with related ones., Comment: 19 pages, 6 figures

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the $R$-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm. The results presented in this paper generalize some corresponding known results., Comment: 15 pages, 4 figures

Some estimates for the norm and essential norm of the difference of two composition operators between different Hardy spaces are given in this paper.

In this paper, we characterize the closures of Dirichlet type spaces D α in the logarithmic Bloch space. Moreover, we study the boundedness and compactness of composition operators from the logarithmic Bloch space to closures of Dirichlet type spaces D α in the logarithmic Bloch space.

The boundedness, compactness and essential norm of weighted composition operators from H∞ to the Bloch space in the unit ball of Cn are investigated in this paper. In particular, some new character...

We characterize the closure of Dirichlet type spaces Dμ in Bloch type spaces. Moreover, we study the boundedness and compactness of composition operators from Bloch type spaces to closures of Dirichlet type spaces Dμ in Bloch type spaces.

Let μ be a nonnegative Borel measure on the unit disk 𝔻 {\mathbb{D}} . In this paper, we investigate measures μ such that the weighted BMOA {\mathrm{BMOA}} spaces are embedded boundedly or compactly into tent-type spaces 𝒯 φ ∞ ⁢ ( μ ) {\mathcal{T}_{\varphi}^{\infty}(\mu)} . As an application, we characterize the boundedness and compactness of Volterra integral operators on the weighted BMOA {\mathrm{BMOA}} space.

Under some mild conditions on the weight function $$\rho $$ , we characterize lacunary series in Dirichlet-type spaces. Moreover, we also obtain a new characterization of Dirichlet-type spaces in terms of pseudoanalytic extension. Two applications are also given.

In this paper, we give some estimates for the essential norm of weighted composition operators from the Bloch space and the Zygmund space to the Bloch space.