Mapping properties of the elliptic maximal function

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We prove that the elliptic maximal function maps the Sobolev space W4,η(ℝ2) into L4(ℝ2) for all η > 1/6. The main ingredients of the proof are an analysis of the intersection properties of elliptic annuli and a combinatorial method of Kolasa and Wolff.

Original languageEnglish (US)
Pages (from-to)221-234
Number of pages14
JournalRevista Matematica Iberoamericana
Issue number1
StatePublished - 2003
Externally publishedYes


  • Circular maximal function
  • Multiparameter maximal functions
  • Sobolev space estimates

ASJC Scopus subject areas

  • Mathematics(all)


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