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Rough maximal singular integral and maximal operators supported by subvarieties

Daiqing Zhang
대한수학회 (The Korean Mathematical Society)|2021.03|대한수학회보 (Bulletin of the KMS)|제58권 제2호|pp. 277-303|DOI 10.4134/BKMS.b200008

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참고문헌

키워드

rough kernelMaximal singular integralmaximal operatorpolynomial mappingsTriebel-Lizorkin spaces and Besov spaces
주제분류수학

초록

Under the rough kernels $\Omega$ belonging to the block spaces $B_{r}^{0,q}({\rm S}^{n-1})$ or the radial Grafakos-Stefanov kernels $W\mathcal{F}_\beta({\rm S}^{n-1})$ for some $r,\,\beta>1$ and $q\leq 0$, 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 \cite{LXY1,LXY2}, in which the authors established the corresponding results under the conditions that the rough kernels belong to the function class $L(\log L)^{\alpha}({\rm S}^{n-1})$ or the Grafakos-Stefanov class $\mathcal{F}_\beta({\rm S}^{n-1})$ for some $\alpha\in[0,1]$ and $\beta\in(2,\infty)$.

Abstract

Under the rough kernels $\Omega$ belonging to the block spaces $B_{r}^{0,q}({\rm S}^{n-1})$ or the radial Grafakos-Stefanov kernels $W\mathcal{F}_\beta({\rm S}^{n-1})$ for some $r,\,\beta>1$ and $q\leq 0$, 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 \cite{LXY1,LXY2}, in which the authors established the corresponding results under the conditions that the rough kernels belong to the function class $L(\log L)^{\alpha}({\rm S}^{n-1})$ or the Grafakos-Stefanov class $\mathcal{F}_\beta({\rm S}^{n-1})$ for some $\alpha\in[0,1]$ and $\beta\in(2,\infty)$.

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