WEIGHTED COMPOSITION OPERATORS ON SPACES OF FUNCTIONS WITH DERIVATIVE IN A HARDY SPACE

Let φ and ψ be two analytic functions defined on D such that φ(D) ⊆ D. The operator given by f ↦ ψ(f ○ φ) is called a weighted composition operator. For each 1 ≤ p ≤ ∞, let Sp be the space of analytic functions on D whose derivatives belong to the Hardy space Hp. In this paper we deal with boundedne...

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Veröffentlicht in:	Journal of operator theory 2004-06, Vol.52 (1), p.173-184
Hauptverfasser:	CONTRERAS, M.D., HERNÁNDEZ-DÍAZ, A.G.
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Sprache:	eng
Schlagworte:	Abstract spaces Algebra Analytic functions Banach space Converse propositions Mathematical theorems Operator theory Property composition Unit ball
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description	Let φ and ψ be two analytic functions defined on D such that φ(D) ⊆ D. The operator given by f ↦ ψ(f ○ φ) is called a weighted composition operator. For each 1 ≤ p ≤ ∞, let Sp be the space of analytic functions on D whose derivatives belong to the Hardy space Hp. In this paper we deal with boundedness, compactness, weak compactness, and complete continuity of weighted composition operators from Sp into Sq for 1 ≤ p, q ≤ ∞.
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subjects	Abstract spaces Algebra Analytic functions Banach space Converse propositions Mathematical theorems Operator theory Property composition Unit ball
title	WEIGHTED COMPOSITION OPERATORS ON SPACES OF FUNCTIONS WITH DERIVATIVE IN A HARDY SPACE
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