Smoothness properties of functions in R 2 ( x ) at certain boundary points

Edwin Wolf

International Journal of Mathematics and Mathematical Sciences, 1979, vol. 2, 1-12

Abstract:

Let X be a compact subset of the complex plane ℂ . We denote by R 0 ( X ) the algebra consisting of the (restrictions to X of) rational functions with poles off X . Let m denote 2 -dimensional Lebesgue measure. For p ≥ 1 , let R p ( X ) be the closure of R 0 ( X ) in L p ( X , d m ) .

In this paper, we consider the case p = 2 . Let x ϵ ∂ X be both a bounded point evaluation for R 2 ( X ) and the vertex of a sector contained in Int X . Let L be a line which passes through x and bisects the sector. For those y ϵ L ∩ X that are sufficiently near x we prove statements about | f ( y ) − f ( x ) | for all f ϵ R 2 ( X ) .

Date: 1979
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:941686

DOI: 10.1155/S0161171279000326

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