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Composition Operators on the Generalized Bergman Space


Affiliations
1 Studentski Trg 16, Beograd-11000, Yugoslavia, Serbia
     

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In this note we prove the following result:
Let ∅: U∅U be analytic and nonconstant and w be convex modulus function. Then the composition operator T(f)=fo∅ on the generalized weighted Bergman space Bw,ω(U) satisfies the inequality.
T(f)‖Bw,ωCfBw,ω

for some C independent of f, where ‖fBw,ω=∫w(|f(z)|)ω(z)dm(z).


Keywords

Composition Operator, Bounded, Modulus Function, The Generalized Bergman Space, Almost Classical Weight.
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  • Composition Operators on the Generalized Bergman Space

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Authors

Stevo Stevic
Studentski Trg 16, Beograd-11000, Yugoslavia, Serbia

Abstract


In this note we prove the following result:
Let ∅: U∅U be analytic and nonconstant and w be convex modulus function. Then the composition operator T(f)=fo∅ on the generalized weighted Bergman space Bw,ω(U) satisfies the inequality.
T(f)‖Bw,ωCfBw,ω

for some C independent of f, where ‖fBw,ω=∫w(|f(z)|)ω(z)dm(z).


Keywords


Composition Operator, Bounded, Modulus Function, The Generalized Bergman Space, Almost Classical Weight.