International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 3, Pages 415-426

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

Edwin Wolf

Department of Mathematics, East Carolina University, Greenville 27834, North Carolina, USA

Received 31 January 1979

Copyright © 1979 Edwin Wolf. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let X be a compact subset of the complex plane . 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 p1, let Rp(X) be the closure of R0(X) in Lp(X,dm).

In this paper, we consider the case p=2. Let xϵX be both a bounded point evaluation for R2(X) and the vertex of a sector contained in IntX. Let L be a line which passes through x and bisects the sector. For those yϵLX that are sufficiently near x we prove statements about |f(y)f(x)| for all fϵR2(X).