BOUNDEDNESS FOR TOEPLITZ TYPE OPERATOR ASSOCIATED WITH SINGULAR INTEGRAL OPERATOR WITH VARIABLE CALDERÓN-ZYGMUND KERNEL

In this paper, we establish sharp maximal function inequalities for the Toeplitz-type operator associated with the singular integral operator with a variable Calderón-Zygmund kernel. As an application, we obtain the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces.

Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces

LetT1be a generalized Calderón-Zygmund operator or±I(the identity operator), letT2andT4be the linear operators, and letT3=±I. Denote the Toeplitz type operator byTb=T1MbIαT2+T3IαMbT4, whereMbf=bfandIαis the fractional integral operator. In this paper, we investigate the boundedness of the operatorTbon weighted Morrey space whenbbelongs to the weighted BMO spaces.

Weighted boundedness for toeplitz type operators associated to singular integral operator with non-smooth kernel

In this paper, the weighted boundedness of the Toeplitz type operator associated to some singular integral operator with non-smooth kernel on Lebesgue spaces are obtained. To do this, some weighted sharp maximal function inequalities for the operator are proved.