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
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