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Distance of a Bloch Function to the Little Bloch Space

Published online by Cambridge University Press:  17 April 2009

Maria Tjani
Maria Tjani
Affiliation:
Department of Mathematical SciencesUniversity of ArkansasFayetteville, AR 72701United States of America e-mail: mtjani@uark.edu
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Motivated by a formula of P. Jones that gives the distance of a Bloch function to BMOA, the space of bounded mean oscillations, we obtain several formulas for the distance of a Bloch function to the little Bloch space, β0. Immediate consequences are equivalent expressions for functions in β0. We also give several examples of distances of specific functions to β0. We comment on connections between distance to β0 and the essential norm of some composition operators on the Bloch space, β. Finally we show that the distance formulas in β have Bloch type spaces analogues.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 101 - 119
Copyright
Copyright © Australian Mathematical Society 2006

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