Let T be the singular integral,and be the commutator generated from T and a Lipschitz function.In this paper,we discuss the endpiont estimate for the commutator whose kernel satisfies the Hrmander condition,that is,the commutator is bounded from to BMO.

Endpoint Estimate for Commutators of Singular Integral Operators on Hrmander Condition

It is proved that, for the nondivergence elliptic equations ∑in, j=1 aijuxixj = f,if f belongs to the generalized Morrey spaces Lp,ψ(ω), then uxixj ∈ Lp,ψ(ω), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp,ψ (ω).

Interior estimates in morrey spaces for solutions of elliptic equations and weighted boundedness for commutators of singular integral operators

In this paper, we prove the the continuity for the mul- tilinear commutator associated to the singular integral operator with general kernel on the Besov spaces. AMS Subject Classication (2000). 42B20, 42B25.

Continuity for Multilinear Commutator of Singular Integral Operator with General Kernel on Besov Spaces

In this paper, the boundedness for the multilinear commutators related to the singular integral operator with weighted Lipschitz functions is proved.

Boundedness for Multilinear Commutator of Singular Integral Operator with Weighted Lipschitz Functions

In this paper, we prove some sharp maximal function estimates for the commutators related to certain generalized fractional integral operator with general kernel and the BMO and Lipschitz functions. As an application, we obtain the boundedness of the commutators on Lebesgue, Morrey and Triebel-Lizorkin spaces. The operator includes fractional Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

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Sharp Maximal Function Estimates and Boundedness for Commutator Related to Generalized Fractional Integral Operator

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Boundedness for Multilinear Commutator of Singular Integral Operator with Weighted Lipschitz Functions

Sharp Maximal Function Estimates and Boundedness for Commutator Related to Generalized Fractional Integral Operator