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Composition Operators on the Generalized Bergman Space
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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,ω≤C‖f‖Bw,ω
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,ω≤C‖f‖Bw,ω
for some C independent of f, where ‖f‖Bw,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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