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In this paper, we first establish an abstract inequality for lower order eigenvalues of a self-adjoint operator on a Hilbert space which generalizes and extends the recent results of Cheng et al. (Calc. Var. Partial Differential Equations, 38, 409–416 (2010)). Then, making use of it, we obtain some universal inequalities for lower order eigenvalues of the biharmonic operator on manifolds admitting some special functions. Moreover, we derive a universal inequality for lower order eigenvalues of the poly-Laplacian with any order on the Euclidean space.

In this paper, the concepts of approximate character amenability (contractibility), uniform approximate character amenability (contractibility) and w*-approximate character amenability are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebras. We show that approximate character amenability, w*-approximate character amenability and approximate character contractibility are the same properties, as uniform approximate character amenability and character amenability, as uniform approximate character contractibility and character contractibility. The general theory for these concepts is also developed. Moreover, approximate character amenability of several concrete classes of Banach algebras related to locally compact groups and also some discrete semigroups is considered.

In order to study a class of finite-dimensional representations of Uq(sl2), we deal with the quotient algebra Uq(m, n, b) of quantum group Uq(sl2) with relations Kr = 1, Emr = b, Fnr = 0 in this paper, where q is a root of unity. The algebra Uq(m, n, b) is decomposed into a direct sum of indecomposable (left) ideals. The structures of indecomposable projective representations and their blocks are determined.

In this paper, using an equivalent characterization of the Besov space by its wavelet coefficients and the discretization technique due to Maiorov, we determine the asymptotic degree of the Bernstein n-widths of the compact embeddings Open image in new window , where \(B_{q_0 }^{s + t} (L_{p_0 } (\Omega ))\) is a Besov space defined on the bounded Lipschitz domain Ω ⊂ ℝd. The results we obtained here are just dual to the known results of Kolmogorov widths on the related classes of functions.

In this paper, we show that certain generalized free products of nilpotent-by-finite groups are subgroup separable when the amalgamated subgroup is 〈h〉×D where D is in the center of both factors.

In this paper, we prove Beurling’s theorem for NA groups, from which we derive some other versions of uncertainty principles.

In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz and Ambrosetti-Coti Zelati with (PSC)c type condition of Palais-Smale-Cerami to study the existence of new periodic solutions with a prescribed energy for symmetrical singular second order Hamiltonian conservative systems with weak force type potentials.

In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space $\dot L_\gamma ^p $ (ℝ n ) to the Lebesgue space L p (ℝ n ) for 1 < p < ∞ and 0 < γ < $\min \{ \tfrac{n} {2},\tfrac{n} {p}\} $ .

In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W*-module \(l_2 \bar \otimes A\), and give a one to one correspondence between the set of positive self-adjoint regular module operators on \(l_2 \bar \otimes A\) and the set of regular quadratic forms, where A is a finite and σ-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup \(\{ T_t \} _{t \in \mathbb{R}^ + } \subset L(l_2 \bar \otimes A)\) is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L(\(l_2 \bar \otimes A\)) is the von Neumann algebra of all adjointable module maps on \(l_2 \bar \otimes A\).

The purpose of this paper is to investigate the growth of meromorphic functions concerning Picard values with a radially distributed value. This generalizes a classic result due to Hayman [Hayman, W. K.: Picard values of meromorphic functions and their derivatives. Ann. of Math., 70, 9–42 (1959)].

In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature.

The main purpose of this paper is to establish some new sufficient conditions under which shift-invariant systems become frames in L 2(ℝ n ). As applications, we obtain new results for Gabor frames.

In this paper, we give a similarity classification for the multiplication operator M g on the Sobolev disk algebra \(R(\mathbb{D})\) with g analytic on the closure of the unit disk \(\mathbb{D}\).

In this paper, we consider the dynamics of the map z ↦ exp(z)/z on the punctured plane ℂ* = ℂ\{0}. We show that for almost every point z ∈ ℂ*, the ω-limit set of z is equal to {0,∞}. In particular, the map is not recurrent.

In this paper, we introduce and study the Sobolev spaces of exponential type associated with the Weinstein operator, via some elements of harmonic analysis related to this operator. In particular, some properties, including completeness and imbedding theorem, are proved. Finally, using the theory of reproducing kernels, some applications are given for these spaces.

We discuss the higher dimensional Bonnesen-style inequalities. Though there are many Bonnesen-style inequalities for domains in the Euclidean plane ℝ2 few results for general domain in ℝn (n ≥ 3) are known. The results obtained in this paper are for general domains, convex or non-convex, in ℝn.

Let (g, (p)) be a restricted Lie algebra over an algebraically closed field of characteristic p> 0. Then the inverse limits of "higher" reduced enveloping algebras {uχs (g) | s ∈ N} with χ running over g ∗ make representations of g split into different "blocks". In this paper, we study such an infinite- dimensional algebra Aχ(g) := lim − Uχs (g )f or a givenχ ∈ g ∗ . A module category equivalence is built between subcategories of U (g)-mod and Aχ(g)-mod. In the case of reductive Lie algebras, (quasi) generalized baby Verma modules and their properties are described. Furthermore, the dimensions of projective covers of simple modules with characters of standard Levi form in the generalized χ-reduced module category are precisely determined, and a higher reciprocity in the case of regular nilpotent is obtained, generalizing the ordinary reciprocity.

In this paper, we study the approximation of identity operator and the convolution integral operator Bm by Fourier partial sum operators, Fejer operators, Vallee-Poussin operators, Cesaro operators and Abel mean operators, respectively, on the periodic Wiener space (C1(ℝ),Wℴ) and obtain the average error estimations.

In this paper, we express the essential norms of composition operators between weighted Bergman spaces of the unit disc in terms of the generalized Nevanlinna counting function.

Let \(\mathcal{A}\) and \(\mathcal{B}\) be unital rings, and \(\mathcal{M}\) be an \(\left( {\mathcal{A},\mathcal{B}} \right)\)-bimodule, which is faithful as a left \(\mathcal{A}\)-module and also as a right \(\mathcal{B}\)-module. Let \(\mathcal{U} = Tri\left( {\mathcal{A},\mathcal{M},\mathcal{B}} \right)\) be the triangular algebra. In this paper, we give some different characterizations of Lie higher derivations on \(\mathcal{U}\).

Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslan- der and Bridger and the Cohen-Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, we establish a relation between the injective dimension of a generalized tilting module ω and the finitistic dimension with respect to ω.

This paper studies the Hardy-type inequalities on the intervals (may be infinite) with two weights, either vanishing at two endpoints of the interval or having mean zero. For the first type of inequalities, in terms of new isoperimetric constants, the factor of upper and lower bounds becomes smaller than the known ones. The second type of the inequalities is motivated from probability theory and is new in the analytic context. The proofs are now rather elementary. Similar improvements are made for Nash inequality, Sobolev-type inequality, and the logarithmic Sobolev inequality on the intervals., 40 pages, 2 figures; Acta Math. Sin. Eng. Ser. 2012

In this paper we get the sharp estimates of the p-adic Hardy and Hardy-Littlewood-Polya operators on L q (|x| dx). Also, we prove that the commutators generated by the p-adic Hardy operators (Hardy-Littlewood-Polya operators) and the central BMO functions are bounded on L q (|x| dx), more generally, on Herz spaces.

In this paper, we characterize the boundedness and compactness of the weighted composition operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators.

Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderon’s identity. This is inspired by the work of discrete Littlewood-Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe’s covering lemma in multiparameter setting.

Krattenthaler, Orsina and Papi provided explicit formulas for the number of ad-nilpotent ideals with fixed class of nilpotence of a Borel subalgebra of a classical Lie algebra. Especially for types A and C they obtained refined results about these ideals with not only fixed class of nilpotence but also fixed dimension. In this paper, we shall follow their algorithm to determine the enumeration of ad-nilpotent b-ideals with fixed class of nilpotence and dimension for orthogonal Lie algebras, i.e., types B and D.

R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces.

In this paper, we mainly discuss the normality of two families of functions concerning shared values and proved: Let F and G be two families of functions meromorphic on a domain D ⊂ ℂ, a1, a2, a3, a4 be four distinct finite complex numbers. If G is normal, and for every f e F, there exists g e G such that f(z) and g(z) share the values a1, a2, a3, a4, then F is normal on D.

In this paper, we consider the real interpolation with a function parameter between martingale Hardy and BMO spaces. An interpolation theorem for martingale Hardy and BMO spaces is formulated. As an application, real interpolation between martingale Lorentz and BMO spaces is given.

In this paper, we study some ergodic theorems of a class of linear systems of interacting diffusions, which is a parabolic Anderson model. First, under the assumption that the transition kernel a = (a(i, j))i,j∈S is doubly stochastic, we obtain the long-time convergence to an invariant probability measure ν h starting from a bounded a-harmonic function h based on self-duality property, and then we show the convergence to the invariant probability measure ν h holds for a broad class of initial distributions. Second, if (a(i, j)) i,j∈S is transient and symmetric, and the diffusion parameter c remains below a threshold, we are able to determine the set of extremal invariant probability measures with finite second moment. Finally, in the case that the transition kernel (a(i, j))i,j∈S is doubly stochastic and satisfies Case I (see Case I in [Shiga, T.: An interacting system in population genetics. J. Math. Kyoto Univ., 20, 213–242 (1980)]), we show that this parabolic Anderson model locally dies out independent of the diffusion parameter c.

In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results are substantial extensions of some known results on Multilinear high dimensional Hardy operator.

In this paper, we study affine spheres which are isotropic and we obtain a complete classification. In particular, we show that all such affine spheres are hyperbolic affine spheres, isometric with SL(3,ℝ)/SO(3), SL(3,ℂ)/SU(3), SU*(6)/Sp(3) or E6(−26)/F4.

In this paper, some classical estimates between the norms of α-Bloch spaces Bα and Lipschitz classes Lip1−α, 0 < α < 1, are improved.

The loop-Witt algebra is the Lie algebra of the tensor product of the Witt algebra and the Laurent polynomial algebra. In this paper we study the universal central extension, derivations and automorphism group for the loop-Witt algebra.

In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality.

In this paper, we present a new proof of the uniqueness of Koebe-Andreev-Thurston theorem. Our method is based on the argument principle in complex analysis and reviews the connection between the circle packing theorem and complex analysis.

In this paper we define a functional as a difference between the right-hand side and left- hand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its properties, such as exponential and logarithmic convexity. We also, state and prove improvements and reverses of new weighted Boas type inequalities. As a special case of our result we obtain improvements and reverses of the Hardy inequality and its dual inequality. We introduce new Cauchy type mean and prove monotonicity property of this mean.

Let q be a sufficiently large integer and χ be a Dirichlet character modulo q. In this paper, we extend the product Πχ(−1)=−1L(1, χ) with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.

The well-known Lyapunov’s theorem in matrix theory/continuous dynamical systems asserts that a square matrix A is positive stable if and only if there exists a positive definite matrix X such that AX+XA* is positive definite. In this paper, we extend this theorem to the setting of any Euclidean Jordan algebra V. Given any element a ∈ V, we consider the corresponding Lyapunov transformation La and show that the P and S-properties are both equivalent to a being positive. Then we characterize the R0-property for La and show that La has the R0-property if and only if a is invertible. Finally, we provide La with some characterizations of the E0-property and the nondegeneracy property.

By a ball-covering B of a Banach space X, wemean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that universal finite representability and B-convexity of X can be characterized by properties of ball-coverings of its finite dimensional subspaces.

In this paper, the concepts of probabilistic normed Riesz space and probabilistic Banach lattice are introduced, and their basic properties are studied. In this context, some continuity and convergence theorems are proved.

In this paper we obtain a criterion under which the bijectivity of the canonical morphism of a weak Galois extension associated to a weak invertible entwining structure is equivalent to the existence of a strong connection form. Also we obtain an explicit formula for a strong connection under equivariant projective conditions or under coseparability conditions.

In this paper, we discuss the rational maps $F_\lambda (z) = z^n + \lambda /z^n ,n \geqslant 2$ with the positive real parameter λ. It is shown that the immediately attracting basin B λ of ∞ for F λ is always a Jordan domain if the Julia set of F λ is not a Cantor set. Furthermore, B λ is a quasidisk if there is no parabolic fixed point on the boundary of B λ . It is also shown that if the Julia set of F λ is connected, then it is locally connected and all Fatou components are Jordan domains. Finally, a complete description to the problem when the Julia set is a Sierpinski curve is given.

In this paper we prove an ɛ0-regularity theorem for mean curvature flow from surface to a flat Riemannian manifold. More precisely, we prove that if the initial energy \(\int_{\Sigma _0 } {|A|^2 \leqslant \varepsilon _0 } \) and the initial area µ0(Σ0) is not large, then along the mean curvature flow, we have \(\int_{\Sigma _t } {|A|^2 \leqslant \varepsilon _0 } \). As an application, we obtain the long time existence and convergence result of the mean curvature flow.

Recently, C.-.C. Yang and I. Laine have investigated finite order entire solutions f of nonlinear differential-difference equations of the form f n + L(z, f) = h, where n ≥ 2 is an integer. In particular, it is known that the equation f(z)2 +q(z)f(z +1) = p(z), where p(z),q(z) are polynomials, has no transcendental entire solutions of finite order. Assuming that Q(z) is also a polynomial and c ∈ ℂ, equations of the form f(z) n +q(z)eQ(z) f(z +c) = p(z) do posses finite order entire solutions. A classification of these solutions in terms of growth and zero distribution will be given. In particular, it is shown that any exponential polynomial solution must reduce to a rather specific form. This reasoning relies on an earlier paper due to N. Steinmetz.

In this paper, the authors establish the boundedness of the multilinear Calderon-Zygmund operator from products of Hardy spaces into Hardy spaces.

In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type (1, 0) in the sense of Hormander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.

In this paper, continuous homogeneous selections for the set-valued metric generalized inverses T∂ of linear operators T in Banach spaces are investigated by means of the methods of geometry of Banach spaces. Necessary and sufficient conditions for bounded linear operators T to have continuous homogeneous selections for the set-valued metric generalized inverses T∂ are given. The results are an answer to the problem posed by Nashed and Votruba.

In this paper, we investigate the Dirichlet problem for Hermitian-Einstein equation on complex vector bundle over almost Hermitian manifold, and we obtain the unique solution of the Dirichlet problem for Hermitian-Einstein equation.

By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl., 124, 187–206 (2005)] established a new version of Ekeland’s variational principle for set-valued maps, which is expressed by the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement of Ha’s version of set-valued Ekeland’s variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev theorem. From the improved Ha’s version, we deduce a Caristi-Kirk’s fixed point theorem and a Takahashi’s nonconvex minimization theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other.