Bilinear oscillatory integrals and boundedness for new bilinear multipliers

Frédéric Bernicot, Pierre Germain

Research output: Contribution to journalArticle

Abstract

We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger; this extends the well-known linear theory of oscillatory integral in some directions. The proof relies on a combination of time-frequency analysis of Coifman-Meyer type with stationary and non-stationary phase estimates. As a consequence of this analysis, we obtain Lebesgue estimates for new bilinear multipliers defined by non-smooth symbols.

Original languageEnglish (US)
Pages (from-to)1739-1785
Number of pages47
JournalAdvances in Mathematics
Volume225
Issue number4
DOIs
StatePublished - Nov 2010

Fingerprint

Oscillatory Integrals
Multiplier
Boundedness
Time-frequency Analysis
Lebesgue Space
Henri Léon Lebésgue
Estimate
Decay
Oscillation
Operator

Keywords

  • Bilinear multipliers
  • Oscillatory integrals

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bilinear oscillatory integrals and boundedness for new bilinear multipliers. / Bernicot, Frédéric; Germain, Pierre.

In: Advances in Mathematics, Vol. 225, No. 4, 11.2010, p. 1739-1785.

Research output: Contribution to journalArticle

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