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


  • Stephen Deterding



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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How to Cite

Deterding, S. (2019). Bounded point derivations on $R^p(X)$ and approximate derivatives. MATHEMATICA SCANDINAVICA, 124(1), 132–148.