文献类型：期刊文献

英文题名：THE COMMUTANT OF A MULTIPLICATION OPERATOR WITH A FINITE BLASCHKE PRODUCT SYMBOL ON THE SOBOLEV DISK ALGEBRA

作者：Zhao, Ruifang[1];Wang, Zongyao[1];Larson, David R.[2]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

年份：2017

卷号：8

期号：3

起止页码：366

外文期刊名：ANNALS OF FUNCTIONAL ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000407475300008)】；

基金：Zhao's work was partially supported by the Fundamental Research Funds for the Central Universities of China and by a grant of the China Scholarship Council.

语种：英文

外文关键词：Sobolev disk algebra; finite Blaschke product; multiplication operator; commutant

摘要：Let R(D) be the algebra generated in the Sobolev space W-22(D) by the rational functions with poles outside the unit disk (D) over bar. This is called the Sobolev disk algebra. In this article, the commutant of the multiplication operator M-B(z) on R(D) is studied, where B(z) is an n-Blaschke product. We prove that an operator A is an element of L(R(D)) is in A'(M-B(z)) if and only if A = Sigma(n)(i=1) M-hi M-Delta(z)(-1) T-i, where {h(i)}(i=1)(n) subset of R(D), and T-i is an element of L(R(D)) is given by (T-ig)(z) - Sigma(n)(j=1) (-1)(i+j) Delta(ij)(z)g(G(j-1)(z)), i = 1, 2,..., n, G(0)(z) equivalent to z.