Integral type operators between logarithmic Bloch-type space and $F(p,q,s)$ space on the unit ball

2013 ◽  
Vol 82 (2) ◽  
pp. 407-423 ◽  
Author(s):  
LI ZHANG ◽  
ZE HUA ZHOU
Keyword(s):  
Unit Ball ◽  
Integral Type ◽  
Type Space ◽  
Bloch Type Space

scholarly journals On a New Integral-Type Operator from the Weighted Bergman Space to the Bloch-Type Space on the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Weighted Bergman Space ◽  
Type Operator ◽  
Upper And Lower Bounds ◽  
Integral Type ◽  
Type Space ◽  
Bloch Type Space

We introduce an integral-type operator, denoted byPφg, on the space of holomorphic functions on the unit ballB⊂ℂn, which is an extension of the product of composition and integral operators on the unit disk. The operator norm ofPφgfrom the weighted Bergman spaceAαp(B)to the Bloch-type spaceℬμ(B)or the little Bloch-type spaceℬμ,0(B)is calculated. The compactness of the operator is characterized in terms of inducing functionsgandφ. Upper and lower bounds for the essential norm of the operatorPφg:Aαp(B)→ℬμ(B), whenp>1, are also given.

scholarly journals Norm and Essential Norm of an Integral-Type Operator from the Dirichlet Space to the Bloch-Type Space on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Dirichlet Space ◽  
Essential Norm ◽  
Operator Norm ◽  
Type Operator ◽  
Integral Type ◽  
Type Space ◽  
Bloch Type Space

Operator norm and essential norm of an integral-type operator, recently introduced by this author, from the Dirichlet space to the Bloch-type space on the unit ball in are calculated here.

scholarly journals ON AN INTEGRAL OPERATOR FROM THE ZYGMUND SPACE TO THE BLOCH-TYPE SPACE ON THE UNIT BALL

2009 ◽  
Vol 51 (2) ◽  
pp. 275-287 ◽  
Author(s):  
STEVO STEVIĆ
Keyword(s):  
Integral Operator ◽  
Unit Ball ◽  
Zygmund Space ◽  
Type Space ◽  
Bloch Type Space

AbstractIn this paper, we introduce an integral operator on the unit ball$\BB\subset\CC^n$. The boundedness and compactness of the operator from the Zygmund space to the Bloch-type space${\mathcal B}_\mu(\BB)$or the little Bloch-type space${\mathcal B}_{\mu,0}(\BB)$are investigated.

scholarly journals ESSENTIAL COMMUTATIVITY OF SOME INTEGRAL AND COMPOSITION OPERATORS

2011 ◽  
Vol 85 (1) ◽  
pp. 143-153
Author(s):  
ZE-HUA ZHOU ◽  
LIANG ZHANG ◽  
HONG-GANG ZENG
Keyword(s):  
Composition Operators ◽  
Integral Operators ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Space ◽  
Type Space ◽  
Bloch Type Space ◽  
Norm Space

AbstractIn general, multiplication of operators is not essentially commutative in an algebra generated by integral-type operators and composition operators. In this paper, we characterize the essential commutativity of the integral operators and composition operators from a mixed-norm space to a Bloch-type space, and give a complete description of the universal set of integral operators. Corresponding results for boundedness and compactness are also obtained.

scholarly journals Weighted Composition Operator from Mixed Norm Space to Bloch-Type Space on the Unit Ball

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yu-Xia Liang ◽  
Ren-Yu Chen
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Weighted Composition Operator ◽  
Mixed Norm ◽  
Mixed Norm Space ◽  
Type Space ◽  
Bloch Type Space ◽  
Norm Space ◽  
Weighted Composition

We discuss the boundedness and compactness of the weighted composition operator from mixed norm space to Bloch-type space on the unit ball ofCn.

Sign in / Sign up

Export Citation Format

Share Document