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 Page view： 33        Net amount： 40 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 Download PDF Full-Text