Compact differences of composition operators on weighted Dirichlet spaces

被引：9

作者：

Allen, Robert F. ^{[1
]}

Heller, Katherine C. ^{[2
]}

Pons, Matthew A. ^{[2
]}

机构：

[1] Univ Wisconsin, Dept Math, La Crosse, WI 54601 USA

[2] North Cent Coll, Dept Math, Naperville, IL 60540 USA

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2014年 / 12卷 / 07期

关键词：

Composition operator; Compact difference; Weighted Dirichlet space; Complex interpolation; COMPLEX INTERPOLATION; LEBESGUE SPACES; COMPONENTS; SPECTRUM;

D O I：

10.2478/s11533-013-0397-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces D-alpha. Specifically we study differences of composition operators on the Dirichlet space D and S-2, the space of analytic functions whose first derivative is in H-2, and then use Caldern's complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

引用

页码：1040 / 1051

页数：12

共 50 条

[1] Compact differences of weighted composition operators on the weighted Bergman spaces
Wang, Maocai
Yao, Xingxing
Chen, Fen
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
[2] Compact differences of weighted composition operators on the weighted Bergman spaces
Maocai Wang
Xingxing Yao
Fen Chen
[J]. Journal of Inequalities and Applications, 2017
[3] WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES
Liu, Xiaosong
Lou, Zengjian
[J]. ACTA MATHEMATICA SCIENTIA, 2013, 33 (04) : 1119 - 1126
[4] WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES
刘小松
娄增建
[J]. Acta Mathematica Scientia, 2013, 33 (04) : 1119 - 1126
[5] Composition operators on weighted Dirichlet spaces
Zorboska, N
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (07) : 2013 - 2023
[6] Compact differences of composition operators on large weighted Bergman spaces
Park, Inyoung
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 479 (02) : 1715 - 1737
[7] Weighted composition operators on weighted Bergman and Dirichlet spaces
Esmaeili, Kobra
Kellay, Karim
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2023, 66 (01): : 286 - 302
[8] Normal weighted composition operators on weighted Dirichlet spaces
Li, Lu
Nakada, Yukihide
Nestor, Douglas
Shang, Wendy
Weir, Rachel
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 423 (01) : 758 - 769
[9] Compact Differences of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions
J. S. Manhas
[J]. Integral Equations and Operator Theory, 2008, 62 : 419 - 428
[10] Compact Differences of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions
Manhas, J. S.
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2008, 62 (03) : 419 - 428

← 1 2 3 4 5 →