Norm of an integral operator on some analytic function spaces on the unit disk

被引:17
作者
Li, Hao [1 ]
Li, Songxiao [2 ]
机构
[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China
[2] JiaYing Univ, Dept Math, Meizhou 514015, Guangdong, Peoples R China
来源
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2013年
基金
中国国家自然科学基金;
关键词
norm; integral operator; analytic function space; WEIGHTED COMPOSITION OPERATORS; LOGARITHMIC BLOCH SPACE; H-INFINITY; DIRICHLET; PRODUCTS;
D O I
10.1186/1029-242X-2013-342
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
If f is an analytic function in the unit disc D, a class of integral operators is defined as follows: I-f(h)(z) = integral(z)(0) f(w)h'(w)dw, h is an element of H(D), z is an element of D. The norm of I-f on some analytic function spaces is computed in this paper.
引用
收藏
页数:7
相关论文
共 36 条
[1]  
Aleman A, 1997, INDIANA U MATH J, V46, P337
[2]  
ALEMAN A, 1995, COMPLEX VARIABLES, V28, P140
[3]  
Aulaskari R., 1995, Analysis, V15, P101
[4]  
Austin A., 2010, THESIS U HAWAI
[5]   Norms of linear-fractional composition operators [J].
Bourdon, PS ;
Fry, EE ;
Hammond, C ;
Spofford, CH .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (06) :2459-2480
[6]   Norm of the multiplication operators from H∞ to the Bloch space of a bounded symmetric domain [J].
Colonna, Flavia ;
Easley, Glenn R. ;
Singman, David .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 382 (02) :621-630
[7]   The norm of a composition operator with linear symbol acting eon the Dirichlet space [J].
Hammond, C .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 303 (02) :499-508
[8]   On the iterated logarithmic Bloch space on the unit ball [J].
Krantz, Steven G. ;
Stevic, Stevo .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (5-6) :1772-1795
[9]   Products of composition and integral type operators from H∞ to the Bloch space [J].
Li, Songxiao ;
Stevic, Stevo .
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2008, 53 (05) :463-474
[10]   Generalized composition operators on Zygmund spaces and Bloch type spaces [J].
Li, Songxiao ;
Stevic, Stevo .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (02) :1282-1295