Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Author: Thomas A. Metzger
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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] L. Bers, Automorphic forms and Poincaré series for infinitely generated Fuchsian groups, Amer. J. Math. 87 (1965), 196-214. MR 30 #4837. MR 0174737 (30:4937)
  • [2] -, A non-standard integral equation with applications to quasiconformal mappings, Acta Math. 116 (1966), 113-134. MR 33 #273. MR 0192046 (33:273)
  • [3] P. L. Duren, Theory of $ {H^p}$ spaces, Pure and Appl. Math., vol. 38, Academic Press, New York, 1970. MR 42 #3552. MR 0268655 (42:3552)
  • [4] M. I. Knopp, A corona theorem for automorphic forms and related results, Amer. J. Math. 91 (1969), 599-618. MR 40 #4450. MR 0251219 (40:4450)
  • [5] T. A. Metzger and M. Sheingorn, Polynomial approximations in the Bers' spaces (to appear).
  • [6] M. Sheingorn, Poincaré series of polynomials bounded away from zero on a fundamental region, Amer. J. Math, (to appear). MR 0344455 (49:9194)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A82

Retrieve articles in all journals with MSC: 30A82


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310260-7
Keywords: Polynomial density, Bers spaces
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society