Sharp Function Estimates and Boundedness for Toeplitz Type Operators Associated to General Integral Operator

Abstract

In this paper, we establish the sharp maximal function estimates for the Toeplitz type operators associated to some integral operator with general kernel and the Lipschitz functions. As an application, we obtain the boundedness of the Toeplitz type operators on the Lebesgue, Morrey and Triebel-Lizorkin space. The operator includes the Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.