Zygmund's program: Some partial solutions

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Abstract

We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies a weak type  (1,1)  estimate. This allows us to complete Zygmund’s program of the description of the translation invariant bases of multidimensional intervals in the particular case of products of two cubic intervals. As a conjecture, we suggest a more precise version of Zygmund’s program.
Original languageEnglish
Pages (from-to)1439-1453
Number of pages15
JournalAnnales de l'Institut Fourier
Volume55
Issue number5
DOIs
StatePublished - 2005

Scopus Subject Areas

  • Algebra and Number Theory
  • Geometry and Topology

Keywords

  • Covering lemmas
  • Maximal functions

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