Bounded point derivations on certain function spaces

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume31
Issue number2
DOIs
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 American Mathematical Society.

Keywords

  • Approximate derivative
  • Capacity
  • Monogeneity
  • Point derivation

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Bounded point derivations on certain function spaces'. Together they form a unique fingerprint.

Cite this