Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SINGULAR AND MARCINKIEWICZ INTEGRAL OPERATORS ON PRODUCT DOMAINS

  • Badriya Al-Azri (Department of Mathematics College of Science Sultan Qaboos University) ;
  • Ahmad Al-Salman (Department of Mathematics College of Science Sultan Qaboos University and Department of Mathematics Yarmouk University)
  • Received : 2021.12.15
  • Accepted : 2022.08.17
  • Published : 2023.04.30
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Abstract

In this paper, we prove Lp estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)2 (𝕊n-1 × 𝕊m-1). Furthermore, we prove Lp estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

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References

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