TY - JOUR
AU - Deterding, Stephen
PY - 2019/01/13
Y2 - 2023/09/26
TI - Bounded point derivations on $R^p(X)$ and approximate derivatives
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 124
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-109998
UR - https://www.mscand.dk/article/view/109998
SP - 132-148
AB - <p>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 $X$.</p>
ER -