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Volume 36, Issue 1
A Note on Rough Parametric Marcinkiewicz Functions

Laith Hawawsheh, Ahmad Al-Salman & Shaher Momani

Anal. Theory Appl., 36 (2020), pp. 52-59.

Published online: 2020-05

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  • 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) $.

  • AMS Subject Headings

42B20, 42B15, 42B25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Laith.hawawsheh@gju.edu.jo (Laith Hawawsheh)

alsalman@squ. edu.om (Ahmad Al-Salman)

s.momani@ju.edu.jo (Shaher Momani)

  • BibTex
  • RIS
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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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