IJPAM: Volume 115, No. 4 (2017)

Title

$L^p$ BOUNDS FOR MARCINKIEWICZ INTEGRALS
ALONG SURFACES AND EXTRAPOLATION

Authors

Hiyam Al-Bataineh$^1$, Mohammed Ali$^2$
$^{1,2}$Department of Mathematics and Statistics
Jordan University of Science and Technology
Irbid, JORDAN

Abstract

In this article, we study the $L^p$ estimates of Marcinkiewicz integral operators when the kernels belong to $L^{q}\left( \mathbf{S}%
^{n-1}\right)$ for some $q>1$. These estimates allow us to use an extrapolation argument to establish the $L^p$ boundedness of Marcinkiewicz integrals when their kernels in $ L(\log L)^{1/2}(
\mathbf{S}
^{n-1})\cup B^{(0,-1/2)}_q( \mathbf{S}^{n-1})$ with $q>1$. Our results are essential improvements and extensions of some known results on Marcinkiewicz integrals.

History

Received: February 1, 2017
Revised: May 7, 2017
Published: August 10, 2017

AMS Classification, Key Words

AMS Subject Classification: 40B20, 40B15, 40B25
Key Words and Phrases: $L^p$ boundedness, Marcinkiewicz integrals, rough kernels, extrapolation

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Bibliography

1
H. Al-Qassem and A. Al-Salman, A note on Marcinkiewiczintegral operators, J. Math. Anal. Appl., 282(2) (2003),698-710.

2
H. Al-Qassem and Y. Pan, $L^{p}$ estimates for singularintegrals with kernels belonging to certain block spaces, Rev.Mat. Iberoamericana, 18(3) (2002), 701-730.

3
H. Al-Qassem and Y. Pan, On certain estimates forMarcinkiewicz integrals and extrapolation, Collec. Math., 60

How to Cite?

DOI: 10.12732/ijpam.v115i4.11 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 4
Pages: 777 - 786


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