Dini-type Condition Of The Singular Integral Operator Weighted Norm Inequalities

The study of weighted inequalities for singular integral operators has played a central role in modern harmonic analysis since they appear in duality arguments [l].The study of weighted norm inequalities for singular integral operators with standard kernel has gotten many satisfying results. In this paper,we will focus on singular integral operators with Dini-type condition:In this paper,we get the weighted norm inequalities of T as following: (1) Strong (p,p) weighted norm inequality:for any weight ω, and 1 < p < ∞,(2) Weak-type (1,1) two weights estimate:for any weight ω(3) the estimate of H~1(Rn) —> L~1 (R~n) :where H~1(μ) is the atom Hardy space about μ. (4) the weak-type (p,p) two weights estimate:Further,this result is sharp since it does not hold in general when δ = 0 .