Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains

Version 1 : Received: 26 April 2023 / Approved: 27 April 2023 / Online: 27 April 2023 (04:35:49 CEST)

A peer-reviewed article of this Preprint also exists.

Ali, M.; Al-Qassem, H. Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains. Axioms 2023, 12, 596. Ali, M.; Al-Qassem, H. Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains. Axioms 2023, 12, 596.

Abstract

We prove Lp estimates of a class of generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these estimates along with an extrapolation argument we obtain the boundedness of our operators under very weak conditions on the kernel functions. Our results in this paper improve and extend several known results on both generalized Marcinkiewicz integrals and parabolic Marcinkiewicz integrals on product domains.

Keywords

Triebel-Lizorkin space; rough kernel; parabolic Marcinkiewicz integral; product domains; extrapolation

Subject

Computer Science and Mathematics, Analysis

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