Functions in the space R 2 ( E ) at boundary points of the interior

Edwin Wolf

International Journal of Mathematics and Mathematical Sciences, 1983, vol. 6, 1-8

Abstract:

Let E be a compact subset of the complex plane ℂ . We denote by R ( E ) the algebra consisting of (the restrictions to E of) rational functions with poles off E . Let m denote 2 -dimensional Lebesgue measure. For p ≥ 1 , let R p ( E ) be the closure of R ( E ) in L p ( E , d m ) .

In this paper we consider the case p = 2 . Let x ϵ ∂ E be a bounded point evaluation for R 2 ( E ) . Suppose there is a C > 0 such that x is a limit point of the set s = { y | y ϵ Int E , Dist ( y , ∂ E ) ≥ C | y − x | } . For those y ϵ S sufficiently near x we prove statements about | f ( y ) − f ( x ) | for all f ϵ R ( E ) .

Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:142179

DOI: 10.1155/S0161171283000319

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