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$\unicode[STIX]{x1D6F7}$-CARLESON MEASURES AND MULTIPLIERS BETWEEN BERGMAN–ORLICZ SPACES OF THE UNIT BALL OF $\mathbb{C}^{n}$

Part of: Linear function spaces and their duals Holomorphic functions of several complex variables

Published online by Cambridge University Press:  22 March 2017

BENOÎT F. SEHBA Open the ORCID record for BENOÎT F. SEHBA [Opens in a new window]
BENOÎT F. SEHBA*
Affiliation:
Department of Mathematics, University of Ghana, Legon, P.O. Box LG 62, Legon Accra, Ghana email bfsehba@ug.edu.gh
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Abstract

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We define the notion of $\unicode[STIX]{x1D6F7}$-Carleson measures, where $\unicode[STIX]{x1D6F7}$ is either a concave growth function or a convex growth function, and provide an equivalent definition. We then characterize $\unicode[STIX]{x1D6F7}$-Carleson measures for Bergman–Orlicz spaces and use them to characterize multipliers between Bergman–Orlicz spaces.

Keywords

Bergman–Orlicz spacesCarleson measuresmultipliers

MSC classification

Primary: 32A36: Bergman spaces 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 32A35: $H^p$-spaces, Nevanlinna spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 104 , Issue 1 , February 2018 , pp. 63 - 79
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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