Weighted Lp Boundedness of Pseudodifferential Operators and Applications

In this paper we prove weighted norm inequalities with weights in the Ap classes, for pseudodifferential operators with symbols in the class that fall outside the scope of Calderón– Zygmund theory. This is accomplished by controlling the sharp function of the pseudodifferential operator by Hardy–Littlewood type maximal functions. Our weighted norm inequalities also yield Lp boundedness of commutators of functions of bounded mean oscillation with a wide class of operators in .

Sharp function inequalities and boundness for Toeplitz type operator related to general fractional singular integral operator

We establish some sharp maximal function inequalities for the Toeplitz type operator, which is related to certain fractional singular integral operator with general kernel. These results are helpful to investigate the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces respectively.

Weighted Estimates for Maximal Commutators of Multilinear Singular Integrals

This paper is concerned with the pointwise estimates for the sharp function of the maximal multilinear commutatorsTΣb*and maximal iterated commutatorTΠb*, generalized bym-linear operatorTand a weighted Lipschitz functionb. The(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-r))boundedness and the(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-mr))boundedness are obtained for maximal multilinear commutatorTΣb*and maximal iterated commutatorTΠb*, respectively.