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Kyungpook Mathematical Journal 2023; 63(4): 577-591

Published online December 31, 2023 https://doi.org/10.5666/KMJ.2023.63.4.577

Copyright © Kyungpook Mathematical Journal.

A Note on Marcinkiewicz Integral Operators on Product Domains

Badriya Al-Azri, Ahmad Al-Salman*

Sultan Qaboos University, College of Science, Department Mathematics, Muscat, Sultanate of Oman
e-mail : ab8500703@gmail.com

Sultan Qaboos University, College of Science, Department Mathematics, Muscat, Sultanate of Oman
Department of Mathematics, Yarmouk University, Irbid, Jordan
e-mail : alsalman@squ.edu.om or alsalman@yu.edu.jo

Received: May 9, 2022; Revised: June 29, 2023; Accepted: July 5, 2023

Abstract

In this paper we establish the Lp boundedness of Marcinkiewicz integral operators on product domains with rough kernels satisfying a weak size condition. We assume that our kernels are supported on surfaces generated by curves more general than polynomials and convex functions. This generalizes and extends previous results.

Keywords: Marcinkiewicz operators, Product domains, Lp estimates, Maximal functions, Convex functions