On square functions with independent increments and Sobolev spaces on the line

Julià Cufí, Artur Nicolau, Andreas Seeger, Joan Verdera

Research output: Contribution to journalArticleResearchpeer-review

Abstract

© 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany. We prove a characterization of some Lp-Sobolev spaces involving the quadratic symmetrization of the Calderón commutator kernel, which is related to a square function with differences of difference quotients. An endpoint weak type estimate is established for functions in homogeneous Hardy–Sobolev spaces H˙α1. We also use a local version of this square function to characterize pointwise differentiability for functions in the Zygmund class.
Original languageEnglish
Pages (from-to)905-940
JournalAnnali di Matematica Pura ed Applicata
Volume197
Issue number3
DOIs
Publication statusPublished - 1 Jun 2018

Keywords

  • Hardy space
  • Sobolev space
  • Square function
  • Zygmund class

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