Boundedness Of A Class Of Singular Integral Operators And Their Commutators

This thesis contains four chapters,we mainly discuss the boundedness of singular integral operators satisfying a variant Hormander's condition and its multilinear commutators.In chapter 1,we mainly introduce the research background and significance of singular integral operators and commutators,and introduce the definitions of the singular integral operator satisfying a variable Hormander condition and the singular integral operators satisfying a variable LrHormander condition and its commutators.In chapter 2,we mainly discuss the boundedness of singular integral operators satisfying a variable Hormander condition.This chapter consists of two parts,1,the boundedness of singular integral operators satisfying a variable Hormander's condition in generalized Morrey space is proved by Sharp Maximum function estimation;2,the boundedness of singular integral operators satisfying a variable Hormander's condition in weighted Hardy space is proved by atomic decomposition.In chapter 3,we prove the boundedness for multilinear commutators generated by Lipschitz functions with the singular integral operators satisfying a variable Hormander's conditions on Lebesgue spaces,Hardy spaces and Herz-type Hardy spaces.In chapter 4,we study the boundedness for multilinear commutators generated by the Lipschitz functions with the singular integral operators satisfying a variable Lr-Hormander's condition on generalized Morrey space by Sharp Maximum function estimation.