Estimates for functions of generalized Marcinkiewicz operators related to surfaces of revolution

Abstract

In this paper, specific $ L^p $ estimates for generalized Marcinkiewicz operators correlated to surfaces of revolution are proved. These estimates and the extrapolation procedure of Yano are employed to confirm the $ L^p $ boundedness of the above-mentioned integrals under weaker assumptions on the singular kernels. Our findings generalize and improve several known results.

Keywords

• triebel-lizorkin space
• singular kernels
• generalized marcinkiewicz integrals
• $ l^p $ estimates
• extrapolation