Lp bounds for a class of Marcinkiewicz integral operators

Ahmad Al-Salman

doi:10.1216/JIE-2019-31-2-165

L^p bounds for a class of Marcinkiewicz integral operators

Ahmad Al-Salman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we introduce a class of mappings that is more general than the class of polynomials as well as the class of convex functions. We prove L^p estimates of Marcinkiewicz integral operators along surfaces generated by mappings belong to this class. Moreover, we establish the L^p boundedness of the corresponding maximal functions. Our results extend as well as improve previously known results on Marcinkiewicz integral operators and maximal functions.

Original language	English
Pages (from-to)	165-182
Number of pages	18
Journal	Journal of Integral Equations and Applications
Volume	31
Issue number	2
DOIs	https://doi.org/10.1216/JIE-2019-31-2-165
Publication status	Published - 2019
Externally published	Yes

Keywords

at curves
Area integral
Fourier transform
Littlewood-Paley g* functions
Marcinkiewicz integrals
Rough kernels

ASJC Scopus subject areas

Numerical Analysis
Applied Mathematics

Access to Document

10.1216/JIE-2019-31-2-165

Cite this

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keywords = "at curves, Area integral, Fourier transform, Littlewood-Paley g* functions, Marcinkiewicz integrals, Rough kernels",

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AB - In this paper, we introduce a class of mappings that is more general than the class of polynomials as well as the class of convex functions. We prove Lp estimates of Marcinkiewicz integral operators along surfaces generated by mappings belong to this class. Moreover, we establish the Lp boundedness of the corresponding maximal functions. Our results extend as well as improve previously known results on Marcinkiewicz integral operators and maximal functions.

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KW - Area integral

KW - Fourier transform

KW - Littlewood-Paley g functions

KW - Marcinkiewicz integrals

KW - Rough kernels

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