Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ROUGH MAXIMAL SINGULAR INTEGRAL AND MAXIMAL OPERATORS SUPPORTED BY SUBVARIETIES

  • Zhang, Daiqing (School of Computer Science and Mathematics Fujian University of Technology)
  • Received : 2020.01.03
  • Accepted : 2020.12.09
  • Published : 2021.03.31
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Abstract

Under the rough kernels Ω belonging to the block spaces B0,qr (Sn-1) or the radial Grafakos-Stefanov kernels W����(Sn-1) for some r, �� > 1 and q ≤ 0, the boundedness and continuity were proved for two classes of rough maximal singular integrals and maximal operators associated to polynomial mappings on the Triebel-Lizorkin spaces and Besov spaces, complementing some recent boundedness and continuity results in [27, 28], in which the authors established the corresponding results under the conditions that the rough kernels belong to the function class L(log L)α(Sn-1) or the Grafakos-Stefanov class ����(Sn-1) for some α ∈ [0, 1] and �� ∈ (2, ∞).

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