L p -Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels

Abstract

We give the L p -boundedness for a class of Marcinkiewicz integral operators $$ \mu _{\Omega } ,\mu ^{ * }_{{\Omega ,\lambda }} $$ and μΩ,s related to the Littlewood-Paley g-function, $$ g^{ * }_{\lambda } $$ -function and the area integral S, respectively. These operators have the kernel functions Ω∈H 1 (S n−1), the Hardy space on S n−1. These results in this paper substantially improve and extend the known results.