Generalized Weighted Morrey Estimates for Marcinkiewicz Integrals with Rough Kernel Associated with Schrödinger Operator and Their Commutators

Citation:

Ferit G"{U}RB"{U}Z.Generalized Weighted Morrey Estimates for Marcinkiewicz Integrals with Rough Kernel Associated with Schrödinger Operator and Their Commutators[J].Chinese Annals of Mathematics B,2020,41(1):77~98
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Authors:

Ferit G"{U}RB"{U}Z;
Abstract: Let $L=-\Delta+V(x) $ be a Schr\"{o}dinger operator, where $\Delta$ is the Laplacian on ${\mathbb{R}^{n}}$, while nonnegative potential $V(x) $ belonging to the reverse H\"{o}lder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schr\"{o}dinger operator and their commutators. Moreover, the boundedness of the commutator operators formed by {\rm BMO} functions and Marcinkiewicz integrals with rough kernel associated with Schr\"{o}dinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schr\"{o}dinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood (H-L for short) maximal operators, Bochner-Riesz means and parametric {Marcinkiewicz integral} operators which satisfy the conditions of our main results can be considered as some examples.

Keywords:

Marcinkiewicz operator, Rough kernel Schr"{o}dinger operatorgeneralized weighted Morrey space, Commutator, {rm BMO}

Classification:

42B20, 42B35
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