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arXiv · 1709.02851

Bounded point derivations on $R^p(X)$ and approximate derivatives

Stephen Deterding
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Abstract

It is shown that if a point $x_0$ admits a bounded point derivation on $R^p(X)$, the closure of rational function with poles off $X$ in the $L^p(dA)$ norm, for $p >2$, then there is an approximate derivative at $x_0$. A similar result is proven for higher order bounded point derivations. This extends a result of Wang which was proven for $R(X)$, the uniform closure of rational functions with poles off $X$.

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Stephen Deterding. 2017-09-08. Bounded point derivations on $R^p(X)$ and approximate derivatives. https://arxiv.org/abs/1709.02851

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