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2013•Journal of Function Spaces and ApplicationsOpen access

A New Essential Norm Estimate of Composition Operators from Weighted Bloch Space into -Bloch Spaces

René Erlín Castillo, Julio C. Ramos Fernández, Edixon M. Rojas

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Abstract

Let be any weight function defined on the unit disk and let be an analytic self-map of . In the present paper, we show that the essential norm of composition operator mapping from the weighted Bloch space to -Bloch space is comparable to where for , is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003).

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Let be any weight function defined on the unit disk and let be an analytic self-map of . In the present paper, we show that the essential norm of composition operator mapping from the weighted Bloch space to -Bloch space is comparable to where for , is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003).

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Available abstract

Let be any weight function defined on the unit disk and let be an analytic self-map of . In the present paper, we show that the essential norm of composition operator mapping from the weighted Bloch space to -Bloch space is comparable to where for , is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003).

Key concepts: Bloch space, Mathematics, Compact space, Norm (philosophy), Unit disk, Composition (language), Space (punctuation), Composition operator

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