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On polynomial approximation in $ A_{q}(D)$

Author: Thomas A. Metzger
Journal: Proc. Amer. Math. Soc. 37 (1973), 468-470
MSC: Primary 30A82
MathSciNet review: 0310260
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Abstract: Let D be a bounded Jordan domain with rectifiable boundary and define $ {A_q}(D)$, the Bers space, as the space of holomorphic functions f, such that

$\displaystyle \iint\limits_D {\vert f\vert\lambda _D^{2 - q}dx\;dy}$

is finite, where $ {\lambda _D}$ is the Poincaré metric for D. It is shown that the polynomials are dense in $ {A_q}(D)$ for $ q > 3/2$.

References [Enhancements On Off] (What's this?)

  • [1] Lipman Bers, Automorphic forms and Poincaré series for infinitely generated Fuchsian groups, Amer. J. Math. 87 (1965), 196–214. MR 0174737
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  • [3] Peter L. Duren, Theory of 𝐻^{𝑝} spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
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Keywords: Polynomial density, Bers spaces
Article copyright: © Copyright 1973 American Mathematical Society