Bulletin of the
Korean Mathematical Society BKMS

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)