Examples of compactλ-hypersurfaces in Euclidean spaces

In this paper,we first construct compact embeddedλ-hypersurfaces with the topology of torus which are calledλ-torus in Euclidean spaces?n^+1.Then,we give many compact immersedλ-hypersurfaces in Euclidean spaces?n^+1.     

Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups

Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].     

Complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow

In this paper, we study the complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded λ-hypersurfaces with |A|≤α and get some applications of the volume comparison theorem. Secondly, we consider the relation among λ, extrinsic radius k, intrinsic diameter d, and dimension n of the complete λ-hypersurface,and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded λ-hypersurface with some natural and general restrictions.     

Hausdorff Operators on Function Spaces

The authors mainly study the Hausdorff operators on Euclidean space Rn.They establish boundedness of the Hausdorff operators in various function spaces,such as Lebesgue spaces,Hardy spaces,local Hardy ...     

Generalized Rectangular Convexity

In this paper we investigate the tr-convexity and the rectangular biconvexity in Euclidean spaces.     

ON STATIONARY HYPERSURFACES IN EUCLIDEAN SPACES

Some techniques in the Geometric Measure Theory are used to study the hypersurfaces in Euclidean spaces and some fundamental properties with this subject are discussed in this article.     

Complete Space-like λ-surfaces in the Minkowski Space R_1~3 with the Second Fundamental Form of Constant Length

In this paper we study the complete space-like λ-surfaces in the three dimensional Minkowski space R_1~3. As the result, we obtain a complete classification theorem for all the complete space-like λ-surfaces x : M~2→ R_1~3 with the second fundamental form of constant length. This is a natural extension to the λ-surfaces in R_1~3 of a recent interesting classification theorem by Cheng and Wei for λ-surfaces in the Euclidean space R~3.     

Complete Space-like λ-surfaces in the Minkowski Space R1^3 with the Second Fundamental Form of Constant Length

In this paper we study the complete space-like λ-surfaces in the three dimensional Minkowski space R1^3.As the result,we obtain a complete classification theorem for all the complete space-like λ-surfaces x:M^2→R1^3 with the second fundamental form of constant length.This is a natural extension to the λ-surfaces in R1^3 of a recent interesting classification theorem by Cheng and Wei forλ-surfaces in the Euclidean space R^3.     

Function spaces on local fields

We study the function spaces on local fields in this paper, such as Triebel B-type and F-type spaces, Holder type spaces, Sobolev type spaces, and so on, moreover, study the relationship between the p-type derivatives and the Holder type spaces. Our obtained results show that there exists quite difference between the functions defined on Euclidean spaces and local fields, respectively. Furthermore, many properties of functions defined on local fields motivate the new idea of solving some important topics on fractal analysis.     

On Embeddings of Tori in Euclidean Spaces

Using the relation between the set of embeddings of tori into Euclidean spaces modulo ambient isotopies and the homotopy groups of Stiefel manifolds, we prove new results on embeddings of tori into Euclidean spaces.     

变指标中心Morrey空间上带Dini核的多线性C-Z算子（英文）

In this paper, we obtain the boundedness of multilinear Calderón-Zygmund operators with kernels of Dini type and commutators with variable exponent λ-central BMO functions in variable exponent central Morrey spaces.     

On Lawson’s area-minimizing hypercones

We show the area-minimality property of all homogeneous area-minimizing hypercones in Euclidean spaces(classified by Lawlor)following Lawson’s original idea in his 72’Trans.A.M.S.paper"The equivariant Plateau problem and interior regularity".Moreover,each of them enjoys(coflat)calibrations singular only at the origin.     

Radial Operators on the Weighted Bergman Spaces over the Polydisk

In this paper, we study radial operators in Toeplitz algebra on the weighted Bergman spaces over the polydisk by the(m, λ)-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its(0, λ)-Berezin transform on the boundary. In addition, we show that an operator S is radial if and only if its(m, λ)-Berezin transform is a separately radial function.     

POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS

We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.     

Commutators of Lipschitz Functions and Singular Integrals with Non-Smooth Kernels on Euclidean Spaces

In this article, we obtain the L p-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.     

Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions

We construct superprocesses with dependent spatial motion(SDSMs) in Euclidean spaces R^d with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^d,their local times exist when d≤3.A Tanaka formula of the local time is also derived.     

DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B（r,s） ON SOME MADDOX＇S SPACES

The domain of generalized difference matrix B(r, s) in the classical spaces l∞,c, and c0 was recently studied by Kirisci and Bassar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l∞( B, p), c( B, p), and c0( B, p), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces l∞( B, p), c( B, p), and c0( B, p) are computed and the bases of the spaces c( B, p)and c0( B, p) are constructed. The final section of this article is devoted to the characterization of the classes(λ( B, p) :) and( : λ( B, p)), where λ∈ {c, c0, l∞}and is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma.     

Clifford algebra approach to pointwise convergence of Fourier series on spheres Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

We offer an approach by means of Clifford algebra to convergence of Fourier series on unit spheres of even-dimensional Euclidean spaces. It is based on generalizations of Fueter's Theorem inducing quaternionic regular functions from holomorphic functions in the complex plane. We, especially, do not rely on the heavy use of special functions. Analogous Riemann-Lebesgue theorem, localization principle and a Dini's type pointwise convergence theorem are proved.     

λ-Central BMO estimates for multilinear commutators of fractional integrals

The author establishes λ-central BMO estimates for commutators of multilinear fractional integral operators on central Morrey spaces.     

Strict Feasibility of Variational Inequalities in Reflexive Banach Spaces

Strict feasibility is proved to be an equivalent characterization of （dual） variational inequalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This generalizes an earlier result from finite-dimensional Euclidean spaces to infinitedimensional reflexive Banach spaces. Moreover, the monotonicity-type assumptions are also mildly relaxed.