A Note on Rough Parametric Marcinkiewicz Functions

A Note on Rough Parametric Marcinkiewicz Functions

Year:    2020

Author:    Laith Hawawsheh, Ahmad Al-Salman, Shaher Momani

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 1 : pp. 52–59

Abstract

In this note, we obtain sharp $L^{p}$ estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space $L^{1}\left( \mathbb{S}^{n-1}\right) $.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2017-0074

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 1 : pp. 52–59

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Marcinkiewicz integrals parametric Marcinkiewicz functions rough kernels Fourier transform Marcinkiewicz interpolation theorem.

Author Details

Laith Hawawsheh

Ahmad Al-Salman

Shaher Momani

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