A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution

Mohammed Ali and Hussain Al-Qassem ()
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Mohammed Ali: Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
Hussain Al-Qassem: Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, Doha 2713, Qatar

Mathematics, 2022, vol. 10, issue 20, 1-13

Abstract: In this article, certain sharp L p estimates for a specific class of generalized Marcinkiewicz operators with mixed homogeneity associated to surfaces of revolution are established. By virtue of Yano’s extrapolation argument, beside these estimates, the L p boundedness of the aforementioned operators under weaker assumptions on the kernels is confirmed. The obtained results in this article are fundamental extensions and improvements of numerous previously known results on parabolic generalized Marcinkiewicz integrals.

Keywords: extrapolation; Triebel–Lizorkin space; generalized Marcinkiewicz; rough kernels (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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