A note on maximal singular integrals with rough kernels

Abstract

Abstract In this note we study the maximal singular integral operators associated with a homogeneous mapping with rough kernels as well as the corresponding maximal operators. The boundedness and continuity on the Lebesgue spaces, Triebel–Lizorkin spaces, and Besov spaces are established for the above operators with rough kernels in H 1 ( S n − 1 ) $H^{1}({\mathrm{S}}^{n-1})$ , which complement some recent developments related to rough maximal singular integrals.

Keywords

• Maximal singular integral
• Maximal operator
• H 1 ( S n − 1 ) $H^{1}({\mathrm{S}}^{n-1})$
• Homogeneous mapping
• Triebel–Lizorkin space