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September 2018 Marcinkiewicz integrals with rough kernel associated with Schrödinger operators and commutators on generalized vanishing local Morrey spaces
Ferit Gürbüz
Tbilisi Math. J. 11(3): 133-156 (September 2018). DOI: 10.32513/tbilisi/1538532032

Abstract

Let $L=-\Delta+V\left( x\right) $ be a Schrödinger operator, where $\Delta$ is the Laplacian on ${\mathbb{R}^{n}}$, while nonnegative potential $V\left(x\right)$ belonging to the reverse Hölder class. In this paper, using the some conditions on $\varphi\left(x.r\right) $, we dwell on the boundedness of Marcinkiewicz integrals with rough kernel associated with schrödinger operators and commutators generated by these operators and local Campanato functions both on generalized local Morrey spaces and on generalized vanishing local Morrey spaces, respectively. As an application of the above results, the boundedness of parametric Marcinkiewicz integral and its commutator both on generalized local Morrey spaces and on generalized vanishing local Morrey spaces is also obtained.

Citation

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Ferit Gürbüz. "Marcinkiewicz integrals with rough kernel associated with Schrödinger operators and commutators on generalized vanishing local Morrey spaces." Tbilisi Math. J. 11 (3) 133 - 156, September 2018. https://doi.org/10.32513/tbilisi/1538532032

Information

Received: 11 April 2017; Accepted: 15 May 2018; Published: September 2018
First available in Project Euclid: 3 October 2018

zbMATH: 07172281
MathSciNet: MR3954200
Digital Object Identifier: 10.32513/tbilisi/1538532032

Subjects:
Primary: 42B20
Secondary: 42B25, 42B35

Rights: Copyright © 2018 Tbilisi Centre for Mathematical Sciences

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Vol.11 • No. 3 • September 2018
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