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Fractional integration, differentiation, and weighted Bergman spaces

Published online by Cambridge University Press:  01 March 1999

STEPHEN M. BUCKLEY ,
PEKKA KOSKELA  and
DRAGAN VUKOTIĆ
STEPHEN M. BUCKLEY
Affiliation:
Department of Mathematics, National University of Ireland, Maynooth, Co. Kildare, Ireland; e-mail: sbuckley@maths.may.ie
PEKKA KOSKELA
Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35, Fin-40351 Jyväskylä, Finland; e-mail: pkoskela@math.jyu.fi
DRAGAN VUKOTIĆ
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain; e-mail: dragan.vukotic@uam.es
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Abstract

We study the action of fractional differentiation and integration on weighted Bergman spaces and also the Taylor coeffficients of functions in certain subclasses of these spaces. We then derive several criteria for the multipliers between such spaces, complementing and extending various recent results. Univalent Bergman functions are also considered.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 126 , Issue 2 , March 1999 , pp. 369 - 385
Copyright
The Cambridge Philosophical Society 1999

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