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Sharp function inequalities and boundness for Toeplitz type operator related to general fractional singular integral operator

Huang Chuangxia (Department of Mathematics, Changsha University of Science and Technology, Changsha, P.R. of China)
Liu Lanzhe (Department of Mathematics, Changsha University of Science and Technology, Changsha, P.R. of China)

We establish some sharp maximal function inequalities for the Toeplitz type operator, which is related to certain fractional singular integral operator with general kernel. These results are helpful to investigate the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces respectively.