Fractional integration, differentiation, and weighted Bergman spaces

Stephen M. Buckley, Pekka Koskela, Dragan Vukotić

Type: Article

Publication Date: 1999-03-01

Citations: 63

DOI: https://doi.org/10.1017/s030500419800334x

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.

Locations

Mathematical Proceedings of the Cambridge Philosophical Society - View
Maynooth University ePrints and eTheses Archive (Maynooth University) - View - PDF

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Works Cited by This (24)

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+ PDF Chat	$L^{p}$-behaviour of the integral means of analytic functions	1984	Miodrag Mateljević Miroslav Pavlović
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+ PDF Chat	Embedding theorems for spaces of analytic functions via Khinchine's inequality.	1993	Daniel H. Luecking
+	Theorems on Fourier Series and Power Series (II)<sup>†</sup>	1937	J. E. Littlewood R. E. A. C. Paley
+	Differential operator in spaces of analytic functions	1984	A. Zabulionis
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+ PDF Chat	Multipliers on Spaces of Analytic Functions	1995	Óscar Blasco
+ PDF Chat	An extension of the Hausdorff-Young theorem.	1971	Charles N. Kellogg
+ PDF Chat	Zeros of functions in the Bergman spaces	1974	C. J. Horowitz