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 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 On an integral-type operator from Qk(p,q) spaces to α-bloch spaces

Filomat ◽  
2011 ◽  
Vol 25 (3) ◽  
pp. 163-173 ◽  
Author(s):  
Chunping Pan
Keyword(s):  
Integral Operator ◽  
Nonnegative Integer ◽  
Type Operator ◽  
Integral Type ◽  
Bloch Spaces

Let g ? H(D), n be a nonnegative integer and ? be an analytic self-map of D. We study the boundedness and compactness of the integral operator Cn ?,g, which is defined by Cn ?,g f)(z) = ?z0 f(n)(?(?))g(?)d?, z?D, f?H(D), from QK(p,q) and QK,0(p,q) spaces to ?-Bloch spaces and little ?-Bloch spaces.

scholarly journals Riemann-Stieltjes operators between Bergman-type spaces andα-Bloch spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Songxiao Li
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Complex Plane ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Bloch Spaces ◽  
Type Spaces

We study the following integral operators:Jgf(z)=∫0zf(ξ)g′(ξ)dξ;Igf(z)=∫0zf′(ξ)g(ξ)dξ, wheregis an analytic function on the open unit disk in the complex plane. The boundedness and compactness ofJg,Igbetween the Bergman-type spaces and theα-Bloch spaces are investigated.

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