Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces

In this paper, we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in ℱβ(Sn−1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr{F}_{\beta}\left(\mathrm{S}^{n-1}\right)$$\end{document}, a topic that relates to the Grafakos-Stefanov class. The boundedness and continuity of these operators on Triebel-Lizorkin spaces and Besov spaces are discussed.