Arkiv för Matematik

Density of the polynomials in Hardy and Bergman spaces of slit domains

John R. Akeroyd

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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.

Article information

Source
Ark. Mat., Volume 49, Number 1 (2011), 1-16.

Dates
Received: 16 March 2009
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907126

Digital Object Identifier
doi:10.1007/s11512-009-0110-8

Mathematical Reviews number (MathSciNet)
MR2784254

Zentralblatt MATH identifier
1223.30017

Rights
2009 © Institut Mittag-Leffler

Citation

Akeroyd, John R. Density of the polynomials in Hardy and Bergman spaces of slit domains. Ark. Mat. 49 (2011), no. 1, 1--16. doi:10.1007/s11512-009-0110-8. https://projecteuclid.org/euclid.afm/1485907126


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