Hankel matrices acting on Dirichlet spaces

被引：33

作者：

Bao, Guanlong ^{[1
]}

Wulan, Hasi ^{[1
]}

机构：

[1] Shantou Univ, Dept Math, Shantou 515063, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 409卷 / 01期

关键词：

Hankel matrix; Hilbert operator; Dirichlet spaces; Carleson measure; CARLESON MEASURES; OPERATORS;

D O I：

10.1016/j.jmaa.2013.07.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a connection between the Hankel matrix acting on Dirichlet spaces D-alpha, 0 < alpha < 2, and the Carleson measure supported on (-1, 1). As an application, we prove that the generalized Hilbert operators H-beta are always bounded on Dirichlet spaces D-alpha for 0 < alpha < 2 and that the range (0, 2) of alpha in our results is the best possible. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：228 / 235

页数：8

共 20 条

[1] Generalized Hilbert operators on weighted Bergman spaces [J].

Angel Pelaez, Jose ;

Rattya, Jouni .

ADVANCES IN MATHEMATICS, 2013, 240 :227-267

[2]

[Anonymous], 2007, GRADUATE TEXTS MATH

[3]

[Anonymous], 1959, INEQUALITIES

[4]

[Anonymous], 1980, Bull. Lond. Math. Soc, DOI [10.1112/blms/12.3.207, DOI 10.1112/BLMS/12.3.207]

[5]

Arcozzi N, 2002, REV MAT IBEROAM, V18, P443

[6] Carleson measures and some classes of meromorphic functions [J].

Aulaskari, R ;

Wulan, H ;

Zhao, R .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (08) :2329-2335

[7]

Aulaskari R, 1996, ROCKY MT J MATH, V26, P485, DOI 10.1216/rmjm/1181072070

[8] A Characterization of Besov-type Spaces and Applications to Hankel-type Operators [J].

Blasi, Daniel ;

Pau, Jordi .

MICHIGAN MATHEMATICAL JOURNAL, 2008, 56 (02) :401-417

[9] CYCLIC VECTORS IN THE DIRICHLET SPACE [J].

BROWN, L ;

SHIELDS, AL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 285 (01) :269-304

[10] Composition operators and the Hilbert matrix [J].

Diamantopoulos, E ;

Siskakis, AG .

STUDIA MATHEMATICA, 2000, 140 (02) :191-198

← 1 2 →