Boundedness of bilinear multipliers whose symbols have a narrow support

Frédéric Bernicot, Pierre Germain

Research output: Contribution to journalArticle

Abstract

This work is devoted to studying the boundedness on Lebesgue spaces of bilinear multipliers on ℝ whose symbol is narrowly supported around a curve (in the frequency plane). We are looking for the optimal decay rate (depending on the width of this support) for exponents satisfying a sub-Hölder scaling. As expected, the geometry of the curve plays an important role, which is described. This has applications to the bilinear Bochner-Riesz problem (in particular, boundedness of multipliers whose symbol is the characteristic function of a set), as well as to the bilinear restriction-extension problem.

Original languageEnglish (US)
Pages (from-to)165-212
Number of pages48
JournalJournal d'Analyse Mathematique
Volume119
Issue number1
DOIs
StatePublished - 2013

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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