Lp Estimates of certain rough parametric Marcinkiewicz functions

doi:10.1007/s11464-019-0792-6

Front. Math. China

2019, Vol. 14

Issue (5) : 867-879 https://doi.org/10.1007/s11464-019-0792-6

RESEARCH ARTICLE

L^p Estimates of certain rough parametric Marcinkiewicz functions

Laith HAWAWSHEH¹, Ahmad AL-SALMAN²(

)

¹. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan
². Department of Mathematics, Sultan Qaboos University, P. O. Box 36, Al-Khod 123 Muscat, Oman

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Abstract

We prove L^p estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the $L 1 (S n − 1)$ integrability condition. The obtained L^p estimates resolve a problem left open in previous work. Our argument is based on duality technique and direct estimation of operators. As a consequence of our result, we deduce the L^p boundedness of a class of fractional Marcinkiewicz integral operators.

Keywords Marcinkiewicz integrals parametric Marcinkiewicz functions rough kernels Marcinkiewicz interpolation theorem

Corresponding Author(s): Ahmad AL-SALMAN

Issue Date: 22 November 2019

Cite this article:

Laith HAWAWSHEH,Ahmad AL-SALMAN. L^p Estimates of certain rough parametric Marcinkiewicz functions[J]. Front. Math. China, 2019, 14(5): 867-879.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0792-6
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I5/867

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