Sharp function estimates and boundedness for Toeplitz-type operators associated with general fractional integral operators

Abstract

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

Keywords

• toeplitz-type operator
• sharp maximal function
• morrey space
• triebel-lizorkin space
• lipschitz function
• littlewood-paley operator
• marcinkiewicz operator
• bochner-riesz operator
• integral operators
• 42b20
• 42b25