On polynomial approximation in $A_{q}(D)$
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- by Thomas A. Metzger
- Proc. Amer. Math. Soc. 37 (1973), 468-470
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310260-7
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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 \[ \iint \limits _D {|f|\lambda _D^{2 - q}dx\;dy}\] 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
- Lipman Bers, Automorphic forms and Poincaré series for infinitely generated Fuchsian groups, Amer. J. Math. 87 (1965), 196–214. MR 174737, DOI 10.2307/2373231
- Lipman Bers, A non-standard integral equation with applications to quasiconformal mappings, Acta Math. 116 (1966), 113–134. MR 192046, DOI 10.1007/BF02392814
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- Marvin I. Knopp, A corona theorem for automorphic forms and related results, Amer. J. Math. 91 (1969), 599–618. MR 251219, DOI 10.2307/2373341 T. A. Metzger and M. Sheingorn, Polynomial approximations in the Bers’ spaces (to appear).
- Mark Sheingorn, Poincaré series of polynomials bounded away from zero on a fundamental region, Amer. J. Math. 95 (1973), 729–749. MR 344455, DOI 10.2307/2373696
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 468-470
- MSC: Primary 30A82
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310260-7
- MathSciNet review: 0310260