粗糙抛物次线性算子和交换子的抛物广义局部Morrey空间估计（英文）

引入了抛物广义局部Morrey空间,并得到了其上一大类抛物粗糙算子的有界性.还创建了其在抛物广义局部Morrey空间上交换子的抛物局部Campanato空间估计·带粗糙核的抛物次线性算子及其交换子的对应结果可作为特例而得到,作为应用,得到了抛物广义局部Morrev空间上一些解析半群抛物分数次幂的有界特征.     

Morrey型空间刻画和Carleson测度

定义了解析Morrey型空间H_K~p,并利用H~p空间范数给出了其刻画.还运用Carleson测度刻画了从H_K~p到帐篷型空间J_K~p(μ)嵌入映射的有界性及紧性,其中,权函数K:[0,∞)→[0,∞)是一个右连续且非递减的函数.     

多线性Calderón-Zygmund算子的交换子在广义Morrey空间上的紧性

该文研究了多线性ω型Calderón-Zygmund算子与带变量增长条件的广义Campanato空间函数■生成的交换子[■,T]在广义Morrey空间的紧性,给出了[■,T]是从广义Morrey空间的乘积空间到广义Morrey空间的紧算子的充分条件.     

RESEARCH ANNOUNCEMENTS Morrey Regularity of the Solutionto the Dirichlet Problem

To study the local regularity of solutions to second order elliptic partial differential equations, Morrey in [1] introduced some function spaces, which are called the Morrey spaces todaySince then, many mathematicians have studied regularities of solutions to some kinds of secondorder elliptic equations in Morrey spaces.We give the deceptions of Morrey space and weak Morrey space first.Definition 1 Let TheThesubset of those functions of Lp for which will be called the Morrey space LpDefi…     

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.     

p-进中心函数空间及奇异积分算子

引入了几类p-中心函数空间,包括p进A~q和B~q空间、p进λ-中心BMO空间以及p-进中心Morrey空间,得到了p-进A~q空间与B~q空间的对偶性、p-进λ-中心BMO空间和中心Morrey空间的特征,研究了这些空间与加权p-进Lebesgue空间之间的关系.另外,还建立了一类奇异积分算子在p-进中心Morrey空间中的有界性,更进一步,得到了这类算子交换子在p-进中心Morrey空间中的λ-中心BMO估计.     

关于齐次Carnot群上广义Morrey空间中一些性质（英文）

本文研究了关于Heisenberg群上的广义Morrey空间和Carnot群上的Lebesgue空间中Riesz位势算子或者分数阶极大算子的行为.根据Heisenberg群中抽象调和分析方法以及sub Laplacian算子的Dirichlet问题解的表示公式,本文主要给出了关于齐次Carnot群G上消失的广义Morrey空间V L~(p,?)(G)中的加权Hardy算子、分数阶极大算子和分数阶位势算子的有界性刻画.进而也得到无消失模的广义Morrey空间上Morrey位势的浸入不等式.所有这些结果推广了关于Heisenberg群上的广义Morrey空间和Carnot群上的Lebesgue空间中的相关结论.     

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.     

弱Morrey空间与Navier-Stokes方程的强解

本文在弱Morrey空间中考虑Navier-Stokes方程的Cauchy问题.首先在Lorentz空间$L_{p,\infty}={L_p}^{*}(\mathbb{R}^{n})$的基础上定义弱Morrey空间$M^*_{p,\lambda}(\mathbb{R}^n)$(特别地, 若$p>1$, 则$M^*_{p,0}(\mathbb{R}^n)=L_{p,\infty}$),进而研究了弱Morrey空间的基本性质. 其次,证明了热算子$U(t)=e^{t\Delta}$和Calder\’{o}n-Zygmund奇异积分算子在弱Morrey空间的有界性,同时建立了弱Morrey空间上的双线性估计. 最后,利用Kato的方法和压缩映射原理, 证明Navier-Stokes方程的Cauchy问题在弱Morrey空间$M^*_{p,\lambda}(\mathbb{R}^n)$($1相似文献   

具有非倍测度的参数型Marcinkiewicz交换子在Morrey空间的有界性

本文证明了由参数型Marcinkiewicz积分M~p和Lipschitz函数b生成的交换子M_b~p的有界性。在M的核函数满足较强的H(o|¨)rmander条件下,证明了M_b~p不仅从Morrey空间M_p~q(μ)到Morrey空间M_t~s(μ)有界,从Morrey空间M_p~q(μ)到Lipschitz空间Lip_(β-n/p)(μ)有界,而且从Morrey空间M_p~q(μ)到RBMO(μ)有界.     

Multipliers and Morrey Spaces

We study the pointwise multipliers from one Morrey space to another Morrey space. We give a necessary and sufficient condition to grant that the space of those multipliers is a Morrey space as well.     

Doob's inequality,Burkholder-Gundy inequality and martingale transforms on martingale Morrey spaces

We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob's inequality on martingale block spaces, we obtain the Davis' decompositions for martingale Morrey spaces.     

On Stein's extension operator preserving Sobolev–Morrey spaces

We prove that Stein's extension operator preserves Sobolev–Morrey spaces, that is spaces of functions with weak derivatives in Morrey spaces. The analysis concerns classical and generalized Morrey spaces on bounded and unbounded domains with Lipschitz boundaries in the n‐dimensional Euclidean space.     

Trudinger–Moser Type Inequalities with Vanishing Weights in the Unit Ball

We introduce local and global generalized Herz spaces. As one of the main results we show that Morrey type spaces and complementary Morrey type spaces are included into the scale of these Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized Herz spaces with application to Morrey type spaces and their complementary spaces, based on the mentioned inclusion.

     

Q spaces and Morrey spaces

We characterize functions in Morrey space by p-Carleson measures. We then reveal a simple relation between Q space and Morrey space, that is Q space can be viewed as a fractional integration of the Morrey space. Therefore, many results for Morrey space can be translated onto Q space. For example, we show that Q space is a dual space by identifying its predual.     

Strong maximal operator and singular integral operators in weighted Morrey spaces on product domains

We introduce the Morrey spaces on product domains and extend the boundedness of strong maximal operator and singular integral operators on product domains to Morrey spaces.     

The Ahlfors–Beurling transform on Morrey spaces with variable exponents

We establish the vector-valued inequalities of the Ahlfors–Beurling operator on Morrey spaces with variable exponents. As consequences of these inequalities, we have the boundedness of the Ahlfors–Beurling transform on Lebesgue spaces with variable exponents and Morrey spaces. The results obtained in this paper are new in the case of Morrey spaces.     

Singular Integral Operators in Generalized Morrey Spaces on Curves in the Complex Plane

We study the boundedness of the Cauchy singular integral operators on curves in complex plane in generalized Morrey spaces. We also consider the weighted case with radial weights. We apply these results to the study of Fredholm properties of singular integral operators in weighted generalized Morrey spaces.     

本刊英文版Vol.32(2016),No.2论文摘要（英文）

正Some Specific Unboundedness Property in Smoothness Morrey Spaces.The Non-existence of Growth Envelopes in the Subcritical Case Dorothee D.HAROSKE Susana D.MOURA Abstract We study smoothness spaces of Morrey type on R~n and characterise in detail those situations when such spaces of type A_(p,q)~(s,r)(R~n)or A_(u,p,q)~s(R~n)are not embedded into L_∞(R~n).We can show that in the so-called sub-critical,proper Morrey case their growth envelope function