On polynomial approximation in 𝐴_{𝑞}(𝐷)

Metzger, Thomas A.

doi:10.1090/S0002-9939-1973-0310260-7

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
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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

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