International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 3, Pages 415-426
Smoothness properties of functions in at certain boundary points
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 be a compact subset of the complex plane . We denote by the algebra consisting of the (restrictions to of) rational functions with poles off . Let denote -dimensional Lebesgue measure. For , let be the closure of in .
In this paper, we consider the case . Let be both a bounded point evaluation for and the vertex of a sector contained in . Let be a line which passes through and bisects the sector. For those that are sufficiently near we prove statements about for all .