Abstract
In this paper, we establish the sharp maximal function inequalities for the commutators related to some integral operator with general kernel and the and Lipschitz functions. As an application, we obtain the boundedness of the commutators on Lebesgue, Morrey and Triebel-Lizorkin space. The operator includes Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator. MSC:42B20, 42B25.
Highlights
Introduction and preliminariesAs 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 [ – ], the boundedness for the commutators generated by the singular integral operators and Lipschitz functions on Triebel-Lizorkin and Lp(Rn) ( < p < ∞) spaces are obtained
Summary
Introduction and preliminariesAs the development of singular integral operators (see [ – ]), their commutators have been well studied (see [ – ]). In [ – ], the authors prove that the commutators generated by the singular integral operators and BMO functions are bounded on Lp(Rn) for < p < ∞. In [ – ], the boundedness for the commutators generated by the singular integral operators and Lipschitz functions on Triebel-Lizorkin and Lp(Rn) ( < p < ∞) spaces are obtained.
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