加权共合空间(Lqω, Lp)α(Rn) 上一些算子交换子的有界性研究.pdfVIP

Research on Boundedness of Commutators of some Operators on weighted amalgam ( L ^ , L p ) a ( R n ) spaces Abstract In this thesis, we m ain ly study the boundedness o f some operators and th e ir com m utators on weighted am algam (L-^, L p)a (R n) spaces. F irs tly , we use the nature o f A p weight and H older inequality to discuss the boundedness o f singular integral operators w ith rough kernel and its com m utator w ith B M O functions on weighted (L-^, L p ) a ( R n ) spaces. Secondly ,applying the sim ilar methods, we consider the bound­ edness of Bochner-Riesz operators and the com m utator form ed by B M O functions and Bochner-Riesz operators on weighted (L ^ , L p)a (R n) spaces. F in a lly ,w ith the help of John-N irenberg inequality, we prove th a t the boundedness of the com m utator gen­ erated by singular integral operators w ith oscillating kernel and B M O functions on weighted (L-^, L p)a (R n) spaces. Keywords: weighted am algam space; rough kernel; singular integrals; com­ m utator; Ap weight; Bochner-Riesz operators;oscillating kernel Subject Classifcation(AMS 20 00): 42B20, 42B35 万方数据 录 -T^r. J3 I ..1.. * ~ 早 5 |目丄 § i . i 研究背景 1 § 1 . 2 基本概念 3 § 1 . 3 相关引理 4 第二章具有粗糖核的奇异积分算子及其交换子在加权共合空间 ( L t , L p ) a ( R n ) 上的有界性 7 § 2 . 1 具有粗糙核的奇异积分算子在加权（L t , L p)a (R n)空间上的有界性 7