Boundedness of Toeplitz Type Operator Related to Fractional and Singular Integral Operators Satisfying a Variant of H¨ormander’s Condition

In this paper, some sharp maximal function inequalities for the Toeplitz type operator related to the fractional and singular integral operators satisfying a variant of H¨ormander’s condition are proved. As an application, we obtain the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces.