Functions of bounded second p p -variation

Sorina Barza, Pilar Silvestre Albero

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

The generalized functionals of Merentes type generate a scale of spaces connecting the class of functions of bounded second p p -variation with the Sobolev space of functions with p-integrable second derivative. We prove some limiting relations for these functionals as well as sharp estimates in terms of the fractional modulus of order 2 - 1 / p. These results extend the results in Lind (Math Inequal Appl 16:2139, 2013) for functions of bounded variation but are not consequence of the last.

Original languageEnglish
Pages (from-to)69-91
Number of pages23
JournalREVISTA MATEMATICA COMPLUTENSE
Volume27
Issue number1
DOIs
Publication statusPublished - Jan 2014
MoE publication typeA1 Journal article-refereed

Keywords

  • Bounded (second)
  • Bounded second (p, α) variation
  • Fractional moduli of continuity
  • Modulus of p p -continuity
  • Partition
  • Periodic function
  • Steklov averages

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