L p Bounds for Rough Maximal Operators along Surfaces of Revolution on Product Domains

Mohammed Ali and Hussain Al-Qassem ()
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Mohammed Ali: Department of Mathematics and Statistics, Faculty of Science and Arts, Jordan University of Science and Technology, P.O. Box 3030, 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, 2024, vol. 12, issue 2, 1-10

Abstract: In this paper, we study the boundedness of rough Maximal integral operators along surfaces of revolution on product domains. For several classes of surfaces, we establish appropriate L p bounds of these Maximal operators under the assumption Ω ∈ L q ( S m − 1 × S n − 1 ) for some q > 1 , and then we employ these bounds along with Yano’s extrapolation argument to obtain the L p boundedness of the aforementioned integral operators under a weaker condition in which Ω belongs to either the space B q ( 0 , 2 τ ′ − 1 ) ( S m − 1 × S n − 1 ) or to the space L ( l o g L ) 2 / τ ′ ( S m − × S n − 1 ) . Our results extend and improve many previously known results.

Keywords: product spaces; surfaces of revolution; rough kernels; Maximal integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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