A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation

Caterina Maniscalco, Caterina Maniscalco

Research output: Contribution to journalArticle

Abstract

In this paper we introduce the notion of$\Phi$-bounded variation for metric space valued mappings defined on a subset of the real line. Such a notion generalizes the onefor real functions introduced by M. Schramm, and many previous generalized variations. We prove a structural theorem for mappings of $\Phi$-bounded variation. As an application we show that each mapping of $\Phi$-bounded variation defined on a subset of $\RB$possesses a $\Phi$-variation preserving extension to the whole real line.
Original languageEnglish
Pages (from-to)79-90
Number of pages12
JournalReal Analysis Exchange
Volume35
Publication statusPublished - 2009

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

Fingerprint Dive into the research topics of 'A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation'. Together they form a unique fingerprint.

  • Cite this