Some characterizations for exponentially weighted Bergman spaces

被引：6

作者：

Cho, Hong Rae ^{[1
]}

Park, Soohyun ^{[1
]}

机构：

[1] Pusan Natl Univ, Dept Math, Busan, South Korea

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2019年 / 64卷 / 10期

关键词：

Exponentially weighted Bergman space; Lipschitz type characterization; double integral characterization; symmetric lifting operator; UNIT BALL;

D O I：

10.1080/17476933.2018.1553038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize weighted Bergman spaces for the exponential weight omega(alpha,beta) (z) = (1 - vertical bar z vertical bar(2))(alpha) exp(-beta/(1 - vertical bar z vertical bar(2))) when alpha is real and beta is positive. In this paper, two types of characterizations in terms of Lipschitz type conditions and double integral conditions are presented. We also obtain boundedness of the symmetric lifting operator by using the Lipschitz type characterizations.

引用

收藏

页码：1758 / 1772

页数：15

相关论文

共 14 条

[1] New Characterizations for the Weighted Fock Spaces [J].

Choe, Boo Rim ;

Nam, Kyesook .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2019, 13 (06) :2671-2686

[2] Pointwise estimates of weighted Bergman kernels in several complex variables [J].

Dall'Ara, Gian Maria .

ADVANCES IN MATHEMATICS, 2015, 285 :1706-1740

[3] Double Integral Characterization for Bergman Spaces [J].

Hassanlou, Mostafa ;

Vaezi, Hamid .

IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS, 2016, 11 (01) :27-34

[4]

Kohr M, 2005, STUD U BABES-BOL MAT, V50, P129

[5] A Characterization of Bergman Spaces on the Unit Ball of Cn. II [J].

Li, Songxiao ;

Wulan, Hasi ;

Zhu, Kehe .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2012, 55 (01) :146-152

[6] SOME NEW CHARACTERIZATIONS OF WEIGHTED BERGMAN SPACES [J].

Li, Songxiao .

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2010, 47 (06) :1171-1180

[7] A CHARACTERISATION OF BERGMAN SPACES ON THE UNIT BALL OF Cn [J].

Li, Songxiao ;

Wulan, Hasi ;

Zhao, Ruhan ;

Zhu, Kehe .

GLASGOW MATHEMATICAL JOURNAL, 2009, 51 :315-330

[8] HANKEL-OPERATORS ON THE WEIGHTED BERGMAN SPACES WITH EXPONENTIAL-TYPE WEIGHTS [J].

LIN, P ;

ROCHBERG, R .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 1995, 21 (04) :460-483

[9]

Oleinik VL., 1978, J. Soviet Math, V9, P228, DOI [10.1007/BF01578546, DOI 10.1007/BF01578546]

[10] An equivalence for weighted integrals of an analytic function and its derivative [J].

Pavlovic, Miroslav ;

Angel Pelaez, Jose .

MATHEMATISCHE NACHRICHTEN, 2008, 281 (11) :1612-1623