Bounded point derivations on Rp(X) and approximate derivatives

• Stephen Deterding ^[1]
  1. [1] University of Kentucky

     University of Kentucky

     Estados Unidos

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 124, Nº 1, 2019, págs. 132-148
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • It is shown that if a point x0 admits a bounded point derivation on Rp(X), the closure of rational function with poles off X in the Lp(dA) norm, for p>2, then there is an approximate derivative at x0. 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.