Abstract
In this paper, we prove the -type sharp maximal function estimates for the Toeplitz-type operators associated to certain singular integral operators satisfying a variant of Hormander’s condition. As an application, we obtain the weighted boundedness of the operators on the Lebesgue and Morrey spaces. MSC:42B20, 42B25.
Highlights
As the development of singular integral operators, their commutators have been well studied
In [, ], the authors prove that the commutators generated by the singular integral operators and BMO functions are bounded on Lp(Rn) for < p < ∞
In [, ], some Toeplitz-type operators related to the singular integral operators and strongly singular integral operators are introduced, and the boundedness for the operators generated by BMO and Lipschitz functions is obtained
Summary
As the development of singular integral operators (see [ , ]), their commutators have been well studied. In [ , ], the authors prove that the commutators generated by the singular integral operators and BMO functions are bounded on Lp(Rn) for < p < ∞. We prove the sharp maximal function inequalities for the Toeplitz-type operator related to some singular integral operators satisfying a variant of Hörmander’s condition.
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