Rough maximal singular integral and maximal operators supported by subvarieties
Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 277-303
https://doi.org/10.4134/BKMS.b200008
Published online February 24, 2021
Printed March 31, 2021
Daiqing Zhang
Fujian University of Technology
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 $\beta\in(2,\infty)$.
Keywords : Maximal singular integral, maximal operator, polynomial mappings, rough kernel, Triebel-Lizorkin spaces and Besov spaces
MSC numbers : 42B20, 42B25, 42B15, 47G10
Supported by : This work was supported by the Natural Science Foundation of University Union of Science and Technology Department of Fujian Province (No. 2019J01784)
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