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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohammed Ali & Hussain Al-Qassem, 2024. "L p Bounds for Rough Maximal Operators along Surfaces of Revolution on Product Domains," Mathematics, MDPI, vol. 12(2), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:193-:d:1314541
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