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arXiv · 2108.02543

Boundary Smoothness conditions for functions in $R^p(X)$

Stephen Deterding
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Abstract

Let $X$ be a compact subset of the complex plane and let $R^p(X)$, $2< p < \infty$, denote the closure of the rational functions with poles off $X$ in the $L^p$ norm. In this paper we consider three conditions that show how the functions in $R^p(X)$ can have a greater degree of smoothness at the boundary of $X$ than might otherwise be expected. We will show that two of the conditions are equivalent and imply the third but the third does not imply the other two.

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Stephen Deterding. 2021-08-05. Boundary Smoothness conditions for functions in $R^p(X)$. https://arxiv.org/abs/2108.02543

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