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http://dx.doi.org/10.4134/BKMS.b200008

ROUGH MAXIMAL SINGULAR INTEGRAL AND MAXIMAL OPERATORS SUPPORTED BY SUBVARIETIES  

Zhang, Daiqing (School of Computer Science and Mathematics Fujian University of Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 277-303 More about this Journal
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, ∞).
Keywords
Maximal singular integral; maximal operator; polynomial mappings; rough kernel; Triebel-Lizorkin spaces and Besov spaces;
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