Dual of the Class of HKr Integrable Functions

Francesco Tulone, Paul Musial

Research output: Contribution to journalArticlepeer-review

Abstract

We define for 1 <= r < infinity a norm for the class of functions which are Henstock-Kurzweil integrable in the L-r sense. We then establish that the dual in this norm is isometrically isomorphic to L-r' and is therefore a Banach space, and in the case r = 2, a Hilbert space. Finally, we give results pertaining to convergence and weak convergence in this space.
Original languageEnglish
Pages (from-to)151-160
Number of pages10
JournalMinimax Theory and its Applications
Volume4
Publication statusPublished - 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Control and Optimization
  • Computational Mathematics

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