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| Generalized Weighted Morrey Estimates for Marcinkiewicz Integrals with Rough Kernel Associated with Schrödinger Operator and Their Commutators |
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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： 805
Net amount： 710 |
Authors： |
Ferit G"{U}RB"{U}Z; |
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| 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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