一些算子的交换子在广义Morrey空间上的紧性

本文主要研究分数次积分算子、Marcinkiewicz积分、带光滑核的pseudo-differential算子的交换子在广义Morrey空间M_p,ω（Rⁿ）上的紧性.注意它们的处理方法分别不同.     

消失的弱~Morrey 型空间上某些算子的刻画

In this paper we mainly give some characterizations for the boundedness of the weight Hardy operator, maximal operator, potential operator and singular integral operator on the vanishing generalized weak Morrey spaces V W L_Π~(p,φ)(?) with bounded set ?.     

解析Moerry型空间的性质与Toeplitz算子

在广义权函数下,研究了解析Moerry型空间H_K~2的若干性质.与此同时,还研究了H_K~2上的Toeplitz算子.     

Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

In this paper the authors study the boundedness for a large class of sublinear operators \({T_{\alpha}, \alpha \in [0,n)}\) generated by Calderón–Zygmund operators (α = 0) and generated by Riesz potential operator (α > 0) on generalized Morrey spaces \({M_{p,\varphi}}\) . As an application of the above result, the boundeness of the commutator of sublinear operators \({T_{b,\alpha}, \alpha \in [0,n)}\) on generalized Morrey spaces is also obtained. In the case \({b \in BMO}\) and T _b,α is a sublinear operator, we find the sufficient conditions on the pair \({(\varphi_1,\varphi_2)}\) which ensures the boundedness of the operators \({T_{b,\alpha}, \alpha \in [0,n)}\) from one generalized Morrey space \({M_{p,\varphi_1}}\) to another \({M_{q,\varphi_2}}\) with 1/p ? 1/q = α/n. In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on \({(\varphi_1,\varphi_2)}\) , which do not assume any assumption on monotonicity of \({\varphi_1, \, \varphi_2}\) in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular, Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.     

广义加权极大Morrey空间中次线性算子的有界性质

该文给出定义在R~n上的一类广义加权极大Morrey空间.证明一类次线性算子,包括分数次积分算子,在该类空间中的有界性质.同时还研究该类次线性算子的交换子在广义加权极大Morrey空间中的有界性质.     

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.     

一类次线性算子在广义Morrey空间上的加权有界性

本证明了如果次线性算子T在Orlicz空间上有介,则也有Morrey空间上有界,该算子包括极大算子和奇异积分算子等重要算子。     

On Singular Operators in Vanishing Generalized Variable-Exponent Morrey Spaces and Applications to Bergman-Type Spaces

Mathematical Notes - We give a proof of the boundedness of the Bergman projection in generalized variable-exponent vanishing Morrey spaces over the unit disc and the upper half-plane. To this end,...     

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   

次线性算子在一类广义Morrey空间上的有界性及其应用

证明了一组次线性算子及其交换子,如具有粗糙核的Calderón-Zygmund算子、Ricci-Stein振荡奇异积分、Marcinkiewicz积分、分数次积分和振荡分数次积分及其交换子,在一类广义Morrey空间上的有界性.作为应用得到了非散度型椭圆方程在上述Morrey空间的内部正则性.     

几类交换子在广义Morrey空间上的估计

设ωi(x,T)(i=1,2)是Rn×R+上的可测正函数,当(ω1,ω2)∈So,n时,由BMO函数与极大算子M生成的交换子,是从广义Morrey空间Lp,ω1(Rn)到Lp,ω2(Rn)的有界算子.对于奇异积分算子T以及Riesz积分位势算子Iα生成的交换子,也得到了相似的有界性结果.该结论推广了Mizuhara在广义Morrey空间上的相关结论.     

Norm Inequalities in Generalized Morrey Spaces

We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function 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.     

不同Bloch型空间之间的积型算子的紧性

利用Bloch型空间中函数的导数的估计,通过构造一些新的检验函数,运用解析函数的性质与算子理论,给出了不同Bloch型空间中的积型算子紧性的特征.     

Compactness of Commutators of Riesz Potential on Morrey Spaces

In this paper, the authors give a characterization of the (L ^{p, λ} , L ^{q, λ} )-compactness for the Riesz potential commutator [b,I _α ]. More precisely, the authors prove that the commutator [b,I _α ] is a compact operator from the Morrey space L ^{p, λ} (ℝ ⁿ ) to L ^{q, λ} (ℝ ⁿ ) if and only if b ∈ VMO(ℝ ⁿ ), the BMO-closure of . The research was supported by NSF of China (Grant: 10571015, 10826046) and SRFDP of China (Grant: 20050027025).     

Bloch型空间上的广义Volterra型算子的有界性

通过研究Bloch型空间Bα的一些性质,给出了广义复合算子Tφ,g在Bloch型空间Bα(0<α<∞)上有界的充要条件.     

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.     

分数次积分算子的交换子在加权Morrey空间上的一些估计

设0<α(p,k)(w)上的有界性质,其中符号b属于加权BMO空间、Lipschitz空间和加权Lipschitz空间.