On Rough Parametric Marcinkiewicz Integrals Along Certain Surfaces

Mohammed Ali () and Hussain Al-Qassem
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Mohammed Ali: College of Integrative Studies, Abdullah Al-Salem University, Firdous Street, Khaldiya 72303, Kuwait
Hussain Al-Qassem: Department of Mathematics and Statistics, Qatar University, Doha 2713, Qatar

Mathematics, 2025, vol. 13, issue 8, 1-10

Abstract: In this paper, we study rough Marcinkiewicz integrals associated with surfaces defined by Ψ P , ϕ = { ( ˜ P ( w ) , ϕ ( w ) ) : w ∈ R m }. We establish the L p -boundedness of these integrals when the kernel functions lie in the L q ( S m − 1 ) space. Combining this result with Yano’s extrapolation technique, we further obtain the L p -boundedness under weaker kernel conditions—specifically, when the kernels belong to either the block space B q ( 0 , − 1 / 2 ) ( S m − 1 ) or L ( log L ) 1 / 2 ( S m − 1 ) . Our results extend and refine several previously known results on Marcinkiewicz integrals, offering broader applicability and sharper conclusions.

Keywords: Marcinkiewicz integrals; rough operators; L p bounds; extrapolation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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