The Boundedness Of Toeplitz-type Integral Operator With Non-smooth Kernels

In this paper, we mainly study the boundedness and the weighted estimates of the Toeplitz-type operator with non-smooth kernels on several spaces. This paper is constituted with ?vechapters.In chapter 1, we introduce the backgrounds of the Toeplitz-type integral operators and themain results we done in this paper.In chapter 2, we study the boundedness of the Toeplitz-type singular integral operator withnon-smooth kernels on Morrey space. Suppose 1/q = 1/t = p/1 = 1/s =α/n, 1≤q≤p <∞, 1≤t≤s <∞.Then when b∈BMO, we prove that the Toeplitz-type operatorθαb is boundedness from Morreyspace Mqp (Rn) to Mts (Rn).In chapter 3, we study the boundedness of the Toeplitz-type integral operator on non-homogeneous space Lp,λ(μ) : suppose 0 < r <α/n, 1/t = 1/q=αn,λλ12 = qt. Then when b∈RBMO,wehave obtain the Toeplitz-type operatorθαb is bounded from the space Lq,λ2(μ) to Lt,λ1(μ).The mainresults of this paper have been published in Jiangxi Normal University academic journal(Naturalscience edition) 2009,33(6):31-34.In chapter 4, we study three endpoint estimates of the Toeplitz-type singular integral operatorwith non-smooth kernels.In chapter 5, we study the weighted estimates of the Toeplitz-type singular integral operatorwith with non-smooth kernels and the Toeplitz-type with strongly singular Calde′on-Zygmundoperator.