A Note on Rough Parametric Marcinkiewicz Functions
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@Article{ATA-36-52,
author = {Hawawsheh , LaithAl-Salman , Ahmad and Momani , Shaher},
title = {A Note on Rough Parametric Marcinkiewicz Functions},
journal = {Analysis in Theory and Applications},
year = {2020},
volume = {36},
number = {1},
pages = {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) $.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2017-0074}, url = {http://global-sci.org/intro/article_detail/ata/16913.html} }
TY - JOUR
T1 - A Note on Rough Parametric Marcinkiewicz Functions
AU - Hawawsheh , Laith
AU - Al-Salman , Ahmad
AU - Momani , Shaher
JO - Analysis in Theory and Applications
VL - 1
SP - 52
EP - 59
PY - 2020
DA - 2020/05
SN - 36
DO - http://doi.org/10.4208/ata.OA-2017-0074
UR - https://global-sci.org/intro/article_detail/ata/16913.html
KW - Marcinkiewicz integrals, parametric Marcinkiewicz functions, rough kernels, Fourier transform, Marcinkiewicz interpolation theorem.
AB -
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) $.
Hawawsheh , LaithAl-Salman , Ahmad and Momani , Shaher. (2020). A Note on Rough Parametric Marcinkiewicz Functions.
Analysis in Theory and Applications. 36 (1).
52-59.
doi:10.4208/ata.OA-2017-0074
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