Maximal operators and Hilbert transforms along flat curves near L1

Richard Bez

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Abstract

For a class of convex curves in R-d we prove that the corresponding maximal operator and Hilbert transform are of weak type L log L. The point of interest here is that this class admits Curves which are infinitely flat at the origin. We also prove in analogous weak type result for a class of nonconvex hypersurfaces.
Original languageEnglish
Pages (from-to)311-323
Number of pages13
JournalJournal of the Australian Mathematical Society
Volume87
Issue number03
DOIs
Publication statusPublished - 1 Dec 2009

Keywords

  • Hilbert transform
  • maximal operator
  • weak type estimate

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