Vanishing generalized Morrey spaces and commutators of Marcinkiewicz integrals with rough kernel associated with Schrödinger operator

Campanato型空间上与Schrödinger算子相关的Marcinkiewicz积分

Marcinkiewicz integrals associated with Schrödinger operator on Campanato type spaces

该研究建立了与Schrödinger算子相关的Marcinkiewicz积分在局部Morrey-Campanato空间到局部Morrey-Campanato-BLO空间的有界性，并拓展到带粗糙核的情形。

多重线性Littlewood-Paley平方算子及其交换子在加权Morrey空间上的有界性

The multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces

本文证明了多重线性Littlewood-Paley平方算子及其交换子在加权Morrey空间上的有界性，并给出了相关g-函数和Marcinkiewicz积分交换子的推论。

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.

Weighted complete continuity for the commutator of Marcinkiewicz integral

Let $Ω$ be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and $\mathcal{M}_Ω$ be the higher-dimensional Marcinkiewicz integral associated with $Ω$. In this paper, the author considers the complete continuity on weighted $L^p(\mathbb{R}^n)$ spaces with $A_p(\mathbb{R}^n)$ weights, weighted Morrey spaces with $A_p(\mathbb{R}^n)$ weights, for the commutator generated by ${\rm CMO}(\mathbb{R}^n)$ functions and $\mathcal{M}_Ω$ when $Ω$ satisfies certain size conditions.

$B_w^u$-function spaces and their interpolation

We introduce $B_w^u$-function spaces which unify Lebesgue, Morrey-Campanato, Lipschitz, $B^p$, CMO, local Morrey-type spaces, etc., and investigate the interpolation property of $B_w^u$-function spaces. We also apply it to the boundedness of linear and sublinear operators, for example, the Hardy-Littlewood maximal and fractional maximal operators, singular and fractional integral operators with rough kernel, the Littlewood-Paley operator, Marcinkiewicz operator, and so on.

The boundedness of some operators with rough kernel on the weighted Morrey spaces

Let $Ω\in L^q(S^{n-1})$ with $1<q\le\infty$ be homogeneous of degree zero and has mean value zero on $S^{n-1}$. In this paper, we will study the boundedness of homogeneous singular integrals and Marcinkiewicz integrals with rough kernel on the weighted Morrey spaces $L^{p,κ}(w)$ for $q'\le p<\infty$(or $q'<p<\infty$) and $0<κ<1$. We will also prove that the commutator operators formed by a $BMO(\mathbb R^n)$ function $b(x)$ and these rough operators are bounded on the weighted Morrey spaces $L^{p,κ}(w)$ for $q'<p<\infty$ and $0<κ<1$.