On some hyperbolic type equations and weighted anisotropic Hardy operators

We introduce a version of weighted anisotropic Morrey spaces and anisotropic Hardy operators. We find conditions for boundedness of these operators in such spaces. We also reveal the role of these operators in solving some classes of degenerate hyperbolic partial differential equations. Copyright © 2016 John Wiley & Sons, Ltd.     

Littlewood-Paley算子交换子在加权Herz型Hardy空间上的有界性

研究了Littlewood-Paley算子交换子gψ,b在加权Herz型Hardy空间上的性质,并证明了gψ,b在某些条件下是HKa,pq(ω1,ω2)到Ka,pq(ω1,ω2)和HKa,pq(ω1,ω2)到WKa,pq(ω1,ω2)上的有界算子.     

Interpolation theorem on Lorentz spaces over weighted measure spaces

In 1997 Ferreyra proved that it is impossible to extend the Stein-Weiss theorem in the context of Lorentz spaces. In this paper we obtain an interpolation theorem on Lorentz spaces over weighted measure spaces.

     

Uniform Boundedness of Lagrange Operator in Some Weighted Sobolev-Type Space

The authors show the uniform boundedness of the Lagrange operator in some weighted Sobolev-type space.     

Bochner—Riesz算子交换子在加权Morrey空间上的有界性

运用了Sharp极大函数估计的方法证明了当权函数满足一定条件时,Bochner～Riesz算子与加权BMO函数生成的交换子在加权Morrey空间上的有界性．     

Interpolating sequences in harmonically weighted Dirichlet spaces

We describe the interpolating sequences and weak interpolating sequences for the multiplier algebras of harmonically weighted Dirichlet spaces when is a finitely atomic measure.

     

Function spaces of varying smoothness I

This paper deals with function spaces of varying smoothness. It is a modified version of corresponding parts of [8]. Corresponding spaces of positive smoothness s (x) will be considered in part II. We define the spaces B_p (?ⁿ ), where the function ??: x ? s (x) is negative and determines the smoothness pointwise. First we prove basic properties and then we use different wavelet decompositions to get information about the local smoothness behavior. The main results are characterizations of the spaces B_p (?ⁿ ) by weighted sequence space norms of the wavelet coefficients. These assertions are used to prove an interesting connection to the so‐called two‐microlocal spaces C^{s,s ′} (x⁰). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

加权Lipschitz空间上的Littlewood-Paley算子

本文研究了加权Lipschitz空间上的Littlewood-Paley算子.,证明了一个加权Lipschitz 函数在Littlewood-Paley算子下的象或者几乎处处等于无穷或者仍是一个加权Lipschitz函数.     

不同权的Bloch型空间之间的加权复合算子

本文讨论了单位圆上对数Bloch空间β_L和α-Bloch空间β_α之间的加权复合算子uC_φ的有界性和紧性,主要得到以下结论:(i)uC_φ是空间β_L和β_α之间的有界算子或紧算子的充要条件;(ii)uCφ是空间β_L~0和β_α~0之间的有界算子或紧算子的充要条件。     

Morrey Regularity of Solutions to Degenerate Elliptic Equations in Rn

In this paper, we study the Morrey regularity of solutions to the de- generate elliptic equation -(a_{ij}u_{xi})_{xj} = -(f_j)_{xj} in R^n. For this purpose, we introduce four weighted Morrey spaces in R^n.     

Boundedness of the fractional integral on weighted Lebesgue and Lipschitz spaces

Necessary and sufficient conditions are given for the fractional integral operator to be bounded from weighted strong and weak spaces within the range into suitable weighted and Lipschitz spaces. We also characterize the weights for which can be extended to a bounded operator from weighted into a weighted Lipschitz space of order . Finally, under an additional assumption on the weight, we obtain necessary and sufficient conditions for the boundedness of between weighted Lipschitz spaces.

     

The finite Hilbert transform and weighted Sobolev spaces

The boundedness of the finite Hilbert transform operator on certain weighted L_p spaces is well known. We extend this result to give the boundedness of that operator on certain weighted Sobolev spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wavelet expansions forBMOρ (w)‐functions

We give necessary and sufficient conditions on the wavelet coefficients of a function for being a member of some BMO_φ (w) space. We achieve this characterization for a wide variety of wavelet systems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

非交换加权Lorentz空间的对偶空间

设μ是一个半有限von Neumann代数.对于0P∞,0q≤∞,定义了非交换加权Lorentz空间Λ_ω~(p,q)(μ)及其associate空间Λ_ω~(p,q)(μ)',给出了空间Λ_ω~(p,q)(μ)'和Λ_ω~(p,q)(μ)'的一些基本性质.应用这些性质,还给出了非交换加权Lorentz空间Λ_ω~p(μ),0P∞的对偶空间.     

Herz空间中的加权Hardy-Littlewood平均算子

本文给出了加权Hardy-Littlewood平均算子Uψ在Herz空间Kqα,p(Rn)中有界的充分必要条件并估计了相应的算子范数．     

权Herz-morrey空间上的Mareinkiewicz算子

In this paper,the weighted Herz-Morrey spaces are introduced and the estimates for Marcinkiewicz Integrals on the weighted Herz-Morrey spaces are studied.     

Multidimensional rearrangement and Lorentz spaces

We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces. This revised version was published online in June 2006 with corrections to the Cover Date.     

Poincaré's inequality and Sobolev spaces with monomial weights

In this paper, we use a weighted version of Poincaré's inequality to study density and extension properties of weighted Sobolev spaces over some open set $\mathrm{\Omega }\subseteq {\mathbb{R}}^N$. Additionally, we study the specific case of monomial weights $w(x_1,\text{…},x_N)={\prod }_{i=1}^N{\left|x_i\right|}^{a_i},a_i\ge 0$, showing the validity of a weighted Poincaré inequality together with some embedding properties of the associated weighed Sobolev spaces.     

Besov空间到Zygmund空间上的加权复合算子

研究了单位圆盘上的Besov空间B_(p,q)到Zygmund空间Z的加权复合算子u C_φ(u∈Z),利用函数空间上的算子理论相关知识,得到了u C_φ:B_(p,q)→Z的有界性和紧性的充分必要条件.     

Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations

Strong convergence of the numerical solution to a weak solution is proved for a nonlinear coupled flow and transport problem arising in porous media. The method combines a mixed finite element method for the pressure and velocity with an interior penalty discontinuous Galerkin method in space for the concentration. Using functional tools specific to broken Sobolev spaces, the convergence of the broken gradient of the numerical concentration to the weak solution is obtained in the L² norm. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 489–513, 2017