## On polynomial density in $A_{q}(D)$

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- by Thomas A. Metzger
- Proc. Amer. Math. Soc.
**44**(1974), 326-330 - DOI: https://doi.org/10.1090/S0002-9939-1974-0340623-6
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## 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.## References

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*Polynomial approximation in the Bers’ spaces*(to appear).

## Bibliographic Information

- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**44**(1974), 326-330 - MSC: Primary 30A98
- DOI: https://doi.org/10.1090/S0002-9939-1974-0340623-6
- MathSciNet review: 0340623