Arkiv för Matematik

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

John R. Akeroyd

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

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

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2009 © Institut Mittag-Leffler


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.

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