On polynomial density in 𝐴_{𝑞}(𝐷)

Metzger, Thomas A.

doi:10.1090/S0002-9939-1974-0340623-6

On polynomial density in $A_{q}(D)$
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by Thomas A. Metzger PDF

Proc. Amer. Math. Soc. 44 (1974), 326-330 Request permission

Abstract:

Let $D$ be a bounded Jordan domain. Define ${A_q}(D)$, the Bers space, to be the Banach space of holomorphic functions on $D$, such that $\iint _D {|f|\lambda _D^{2 - q}dxdy}$ is finite, where ${\lambda _D}(z)$ is the Poincaré metric for $D$. It is well known that the polynomials are dense in ${A_q}(D)$ for $2 \leqq q < \infty$ and we shall prove they are dense in ${A_q}(D)$ for $1 < q < 2$ if the boundary of $D$ is rectifiable. Also some remarks are made in case the boundary of $D$ is not rectifiable.

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Polynomial approximation in the Bers’ spaces

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