Regularity in Morrey Spaces of Strong Solutions to Nondivergence Elliptic Equations with VMO Coefficients

In this paper, by means of the theories of singular integrals and linear commutators, the authors establish the regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients.     

Parabolic equations with VMO coefficients in generalized Morrey spaces

In this paper, the authors establish the regularity in generalized Morrey spaces of solutions to parabolic equations with VMO coefficients by means of the theory of singular integrals and linear commutators.     

Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.     

齐次Morrey-Herz空间中交换子的中心BMO估计

设T_b为广义Hardy算子和中心BMO函数生成的交换子,本文得到了该交换子在齐次加权Morrey-Herz空间中的有界性.而且,本文给出了带粗糙核的多线形奇异积分算子在齐次Morrey-Herz空间中的中心BMO估计.     

齐型空间上的Morrey空间的算子有界性及其应用

作者建立了一大类次线性算子和交换子在齐型空间上的Morrey空间中的有界性．应用这些结果,作者研究了具有不连续系数的超抛物方程解的局部正则性．     

强奇异积分算子交换子的端点估计

本文考虑强奇异积分算子的交换子在Hardy型空间上的端点估计,建立了这类交换子从H¹（Rⁿ）到弱 L¹（Rⁿ）上的有界性及H¹（Rⁿ）的某个子空间到 L¹（Rⁿ）上的有界性结果.     

Boundedness of Rough Singular Integral Operators on Homogeneous Herz Spaces with Variable Exponents

We establish the boundedness of rough singular integral operators on homogeneous Herz spaces with variable exponents. As an application, we obtain the boundedness of related commutators with BMO functions on homogeneous Herz spaces with variable exponents.     

Bochner-Riesz算子在加权Morrey空间上的一些估计

要本文将得到Bochner-Riesz算子T_R~((n-1)/2)在加权Morrey空间L~(p,k)(w)上的一些强型和弱型估计,1≤P<∞且0相似文献   

分数次积分交换子在Vilenkin群Morrey空间上的有界性

在Vilenkin群上研究了分数次积分与BMO的交换子在Lp空间和Morrey空间上的有界性质.     

奇异积分和位势积分交换子在极大Morrey空间上的有界性

设齐次空间(X,ρ,μ)上定义一类极大Morrey空间L~(p),θ,λ)(X,μ).此类极大Morrey空间是经典的Morrey空间和极大Lebesgue空间的推广.本文考虑了C-Z积分算子、位势算子与BMO函数生成的交换子在该类极大Morrey空间上的有界性.事实上,这些结果甚至在一般的欧式空间上也是新颖的.     

Some Estimates for Convolution Operators with Kernels of Type （l, r） on Homogeneous Groups

Some estimates for the convolution operators with kernels of type （l, r） on Lebesgue spaces with power weights and Herz-type spaces in the setting of homogeneous groups are established.     

分数次积分算子在Vilenkin群Morrey空间上的有界性质

引入了Vilenkin群上弱Morrey空间的概念,得到了分数次积分算子在Vilenkin群Morrey空间上的有界性质,特别地,我们给出了在端点处的弱型估计.     

类奇异积分和交换子在广义Morrey空间上的有界性

The generalized Morrey spaces are introduced under the hypothesis that Rn is endowed with the general parabolic metric , and the boundedness properties are established in generalized Morrey spaces for a class of singular integral operators, which include Calderon-Zygmund singular integrals and their commutators with BMO.     

局部紧Vilenkin群上弱Morrey-Herz空间中一些算子的有界性

首先引入了一个新空间—局部紧Vilenkin群G上弱齐次Morrey-Herz空间WMK_(p,q)~(α,λ)(G),然后在WMK_(p,q)~(α,λ)(G)上讨论了一些奇异积分算子和分数次奇异积分算子的有界性问题.     

Weighted Estimates for the Maximal Commutator of Singular Integral Operator on Spaces of Homogeneous Type

Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.     

Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds,the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases,we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control,then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.     

Boundedness for parabolic singular integral with rough kernels and its commutators on Triebel-Lizorkin spaces

In this paper, the authors give the boundedness on Triebel-Lizorkin spaces for the parabolic singular integral with rough kernel and its commutator.     

某些抛物型算子在加权L~p空间和Morrey空间上的估计

考虑了一致抛物型算子■=_t-∑_(i,j)ⁿ=_1_i(a_(i,j)(x)_j)+V(x),其中势函数V(x)是Rn=_1_i(a_(i,j)(x)_j)+V(x),其中势函数V(x)是Rⁿ(n≥3)上的非负函数,并且属于反霍尔德类.得到了算子(?)的基本解的梯度估计,以及算子V■n(n≥3)上的非负函数,并且属于反霍尔德类.得到了算子(?)的基本解的梯度估计,以及算子V■^(-1),V(-1),V^(1/2)▽■(1/2)▽■^(-1)和V(-1)和V^(1/2)(1/2)^(-1/2)在加权L(-1/2)在加权L^p(Rp(R⁽ⁿ⁺¹⁾)空间和Morrey空间上的估计.     

有变量核的分数次积分算子交换子的CBMO估计(英文)

In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces.     

与分数次积分和具有非光滑的奇异积分算子相关的Toeplitz型算子在Morrey空间的有界性

本文证明了与分数次积分和具有非光滑的奇异积分算子相关的Toeplitz型算子的sharp极大函数估计,做为应用,得到了该算子在Morrey空间的有界性.