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April 2011 Density of the polynomials in Hardy and Bergman spaces of slit domains
John R. Akeroyd
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Ark. Mat. 49(1): 1-16 (April 2011). DOI: 10.1007/s11512-009-0110-8

Abstract

It is shown that for any t, 0< t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that $\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\}$ and with the property that the analytic polynomials are dense in the Bergman space $\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)$ . It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous real-valued function on [0,1], where the polynomials are dense in $H^{t}(\mathbb{D}\setminus\Gamma)$ ; improving upon a result in an earlier paper.

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John R. Akeroyd. "Density of the polynomials in Hardy and Bergman spaces of slit domains." Ark. Mat. 49 (1) 1 - 16, April 2011. https://doi.org/10.1007/s11512-009-0110-8

Information

Received: 16 March 2009; Published: April 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1223.30017
MathSciNet: MR2784254
Digital Object Identifier: 10.1007/s11512-009-0110-8

Rights: 2009 © Institut Mittag-Leffler

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Vol.49 • No. 1 • April 2011
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