Bounded point derivations on certain function spaces

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Let X be a compact nowhere dense subset of the complex plane C, and let dA denote two-dimensional Lebesgue (or area) measure in C. Denote by R(X) the set of all rational functions having no poles on X, and by Rp(X) the closure of R(X) in Lp(X, dA) whenever 1. p < ∞. The purpose of this paper is to study the relationship between bounded derivations on Rp(X) and the existence of approximate derivatives provided 2 < p < ∞ and to draw attention to an anomaly that occurs when p = 2.

Original languageEnglish
Pages (from-to)313-323
Number of pages11
JournalSt. Petersburg Mathematical Journal
Issue number2
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 American Mathematical Society.


  • Approximate derivative
  • Capacity
  • Monogeneity
  • Point derivation

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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