scholarly journals On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Stevo Stević ◽  
Sei-Ichiro Ueki
Keyword(s):  
Holomorphic Function ◽  
Weight Function ◽  
Unit Ball ◽  
Normal Weight ◽  
Type Operator ◽  
Open Unit ◽  
Integral Type ◽  
Open Unit Ball ◽  
Radial Derivative ◽  
Type Spaces

Let𝔹denote the open unit ball ofℂn. For a holomorphic self-mapφof𝔹and a holomorphic functiongin𝔹withg(0)=0, we define the following integral-type operator:Iφgf(z)=∫01ℜf(φ(tz))g(tz)(dt/t),z∈𝔹. Hereℜfdenotes the radial derivative of a holomorphic functionfin𝔹. We study the boundedness and compactness of the operator between Bloch-type spacesℬωandℬμ, whereωis a normal weight function andμis a weight function. Also we consider the operator between the little Bloch-type spacesℬω,0andℬμ,0.

scholarly journals On an Integral-Type Operator from Zygmund-Type Spaces to Mixed-Norm Spaces on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Type Operator ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Space ◽  
Mixed Norm Spaces ◽  
Norm Space ◽  
Type Spaces

The boundedness and compactness of an integral-type operator recently introduced by the author from Zygmund-type spaces to the mixed-norm space on the unit ball are characterized here.

scholarly journals Integral-Type Operators from Bloch-Type Spaces toQKSpaces

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Stevo Stević ◽  
Ajay K. Sharma
Keyword(s):  
Holomorphic Function ◽  
Unit Disk ◽  
Type Operator ◽  
Integral Type ◽  
Bloch Spaces ◽  
Type Spaces

The boundedness and compactness of the integral-type operatorIφ,g(n)f(z)=∫0zf(n)(φ(ζ))g(ζ)dζ,wheren∈N0,φis a holomorphic self-map of the unit diskD,andgis a holomorphic function onD, fromα-Bloch spaces toQKspaces are characterized.

scholarly journals Product Type Operators Involving Radial Derivative Operator Acting between Some Analytic Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2447
Author(s):  
Manisha Devi ◽  
Kuldip Raj ◽  
Mohammad Mursaleen
Keyword(s):  
Multiplication Operator ◽  
Product Type ◽  
Dimensional Euclidean Space ◽  
Open Unit ◽  
Derivative Operator ◽  
Open Unit Ball ◽  
Radial Derivative ◽  
Type Spaces ◽  
Analytic Function Spaces ◽  
Positive Integers

Let N denote the set of all positive integers and N0=N∪{0}. For m∈N, let Bm={z∈Cm:|z|<1} be the open unit ball in the m−dimensional Euclidean space Cm. Let H(Bm) be the space of all analytic functions on Bm. For an analytic self map ξ=(ξ1,ξ2,…,ξm) on Bm and ϕ1,ϕ2,ϕ3∈H(Bm), we have a product type operator Tϕ1,ϕ2,ϕ3,ξ which is basically a combination of three other operators namely composition operator Cξ, multiplication operator Mϕ and radial derivative operator R. We study the boundedness and compactness of this operator mapping from weighted Bergman–Orlicz space AσΨ into weighted type spaces Hω∞ and Hω,0∞.

Holomorphically embedded discs with rapidly growing area

1999 ◽  
Vol 129 (2) ◽  
pp. 343-349
Author(s):  
Josip Globevnik
Keyword(s):  
Unit Ball ◽  
Open Unit ◽  
Open Unit Ball

It is shown that if V is a closed submanifold of the open unit ball of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ 1. It is also shown that if V is a closed submanifold of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ ∞.

Weak-Star Continuous Analytic Functions

1995 ◽  
Vol 47 (4) ◽  
pp. 673-683 ◽  
Author(s):  
R. M. Aron ◽  
B. J. Cole ◽  
T. W. Gamelin
Keyword(s):  
Unit Ball ◽  
Finite Type ◽  
Analytic Functions ◽  
Approximation Property ◽  
Entire Functions ◽  
Open Unit ◽  
Closed Unit Ball ◽  
Open Unit Ball ◽  
Weakly Continuous ◽  
Weak Star

AbstractLet 𝒳 be a complex Banach space, with open unit ball B. We consider the algebra of analytic functions on B that are weakly continuous and that are uniformly continuous with respect to the norm. We show these are precisely the analytic functions on B that extend to be weak-star continuous on the closed unit ball of 𝒳**. If 𝒳* has the approximation property, then any such function is approximable uniformly on B by finite polynomials in elements of 𝒳*. On the other hand, there exist Banach spaces for which these finite-type polynomials fail to approximate. We consider also the approximation of entire functions by finite-type polynomials. Assuming 𝒳* has the approximation property, we show that entire functions are approximable uniformly on bounded sets if and only if the spectrum of the algebra of entire functions coincides (as a point set) with 𝒳**.

Sign in / Sign up

Export Citation Format

Share Document