Smoothness properties of functions in R2(x) at certain boundary points

Let X be a compact subset of the complex plane ℂ. We denote by R0(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 Rp(X) be the closure of R0(X) in Lp(X,dm).

Bibliographic Details
Main Author: Edwin Wolf
Format: Article
Language:English
Published: Hindawi Limited 1979-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171279000326
Description
Summary:Let X be a compact subset of the complex plane ℂ. We denote by R0(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 Rp(X) be the closure of R0(X) in Lp(X,dm).
ISSN:0161-1712
1687-0425