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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On polynomial density in $ A\sb{q}(D)$


Author: Thomas A. Metzger
Journal: Proc. Amer. Math. Soc. 44 (1974), 326-330
MSC: Primary 30A98
MathSciNet review: 0340623
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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 {\vert f\vert\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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0340623-6
PII: S 0002-9939(1974)0340623-6
Keywords: Polynomial density, Bers spaces
Article copyright: © Copyright 1974 American Mathematical Society



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