Lp estimates for the bilinear Hilbert transform

  1. Michael Lacey† and
  2. Christoph Thiele‡
  1. †School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332; and ‡Department of Mathematics, Universität Kiel, D-24118 Kiel, Germany

Abstract

For the bilinear Hilbert transform given by: Formula we announce the inequality ∥H fg∥p3 ≤ K p1 ,p2∥f∥p1∥g∥p2, provided 2 < p 1, p 2 < ∞, 1/p 3 = 1/p 1 + 1/p 2 and 1 < p 3 < 2.

Footnotes

  • Charles Fefferman, Princeton University, Princeton, NJ

  • Abbreviation: CF, Carleson–Fefferman.

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  1. PNAS January 7, 1997 vol. 94 no. 1 33-35
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