The Boundedness Of Some Singular Integral Operators With Weaker Regularity Condition And Their Commutators

In this thesis, we investigate the boundedness of some singular integral operators with weaker regularity condition and their commutators. This thesis is divided into four chapters.In chapter 1, we introduce the background and main results of this thesis. Besides, we also illustrate how and why this topic comes out.In chapter 2, we study the commutator of singular integral operator whose kernel satisfying variant Lr-Hormander condition and prove that Th is bounded on Lp(Rn).In chapter 3, we prove that the Toeplitz operator with variant Lipschitz condition is bounded from Lp(μ) to Lp(v). And we get two weighted estimates of Toeplitz operator satisfying variant Lr-Hormander condition.In chapter 4, we get the boundedness of higher order commutator TbT on weighted Morrey space.