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

Mathematics

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

Keywords

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

ASJC Scopus subject areas

Numerical Analysis
Applied Mathematics

Access to Document

10.1216/JIE-2019-31-2-165

Cite this

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KW - Fourier transform

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KW - Marcinkiewicz integrals

KW - Rough kernels

KW - at curves

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