scholarly journals Bloch-type space of temperature functions on a finite cylinder

2007 ◽  
Vol 5 (3) ◽  
pp. 287-297
Author(s):  
Marcos López-García
Keyword(s):  
Linear Space ◽  
Bergman Space ◽  
Finite Cylinder ◽  
Type Space ◽  
Bloch Type Space

We define the Bloch-type spaceBTas the linear space of temperature functions on the cylinderST=𝕊1×(0,T)such thatsup⁡(x,t)∈T⁡t|∂u∂t(x,t)|<∞,ΩT=[0,2]×(0,T); we prove that(b1(ST))*=BT, whereb1(ST)is the Bergman space of temperature functions onSTbelonging toL1(ΩT,dxdt).

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 Weighted composition operators from Bloch-type into Bers-type spaces

2021 ◽  
Vol 29 (2) ◽  
pp. 243-250
Author(s):  
HAMID VAEZI ◽  
MOHAMAD NAGHLISAR
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Type Space ◽  
Bloch Type Space ◽  
Type Spaces ◽  
Weighted Composition ◽  
Necessary And Sufficient

In this paper we consider the weighted composition operator uC_{\varphi} from Bloch-type space B^{\alpha} into Bers-type space H_{\beta}^{\infty}, in three cases, \alpha>1, \alpha=1 and \alpha<1. We give the necessary and sufficient conditions for boundedness and compactness of the above operator.

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.

Sign in / Sign up

Export Citation Format

Share Document