Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MAXIMAL FUNCTIONS ALONG TWISTED SURFACES ON PRODUCT DOMAINS

  • Al-Salman, Ahmad (Department of Mathematics Sultan Qaboos University Sultanate of Oman and Department of Mathematics Yarmouk University)
  • Received : 2020.09.12
  • Accepted : 2021.02.18
  • Published : 2021.07.31
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Abstract

In this paper, we introduce a class of maximal functions along twisted surfaces in ℝn×ℝm of the form {(𝜙(|v|)u, 𝜑(|u|)v) : (u, v) ∈ ℝn×ℝm}. We prove Lp bounds when the kernels lie in the space Lq (𝕊n-1×𝕊m-1). As a consequence, we establish the Lp boundedness for such class of operators provided that the kernels are in L log L(𝕊n-1×𝕊m-1) or in the Block spaces B0,0q (𝕊n-1×𝕊m-1) (q > 1).

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References

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