Uniform bounds for the bilinear Hilbert transforms, I

Loukas Grafakos, Xiaochun Li

Research output: Contribution to journalArticlepeer-review


It is shown that the bilinear Hilbert transforms H α,β(f,g)(x) = p.v. ∫R f(x - αt)g(x - βt) dt/t map Lp1(R) × Lp2(R) → L p2(R) uniformly in the real parameters α,β when 2 < p1,p2 < ∞ and 1 < p = p1p 2/p1p2 < 2. Combining this result with the main result in [9], we deduce that the operators H1,α map L2(R) × L(R) → L2(R) uniformly in the real parameter α ∈ [0, 1]. This completes a program initiated by A. Calderón.

Original languageEnglish (US)
Pages (from-to)889-933
Number of pages45
JournalAnnals of Mathematics
Issue number3
StatePublished - May 2004
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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