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Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel

Xiaosha ZhouLanzhe Liu — 2013

Colloquium Mathematicae

Some weighted sharp maximal function inequalities for the Toeplitz type operator T b = k = 1 m T k , 1 M b T k , 2 are established, where T k , 1 are a fixed singular integral operator with non-smooth kernel or ±I (the identity operator), T k , 2 are linear operators defined on the space of locally integrable functions, k = 1,..., m, and M b ( f ) = b f . The weighted boundedness of T b on Morrey spaces is obtained by using sharp maximal function inequalities.

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