On the boundedness of the bilinear Hilbert transform along “non-flat” smooth curves. The Banach triangle case

  • Victor Lie

    Purdue University, West Lafayette, USA and Institute of Mathematicsl of the Romanian Academy, Bucharest, Romania
On the boundedness of the bilinear Hilbert transform along “non-flat” smooth curves. The Banach triangle case $(L^r, 1 ≤ r < \infty)$ cover
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Abstract

We show that the bilinear Hilbert transform along curves with is bounded from where are Hölder indices, i.e., , with , and . Here stands for a wide class of smooth "non-flat" curves near zero and infinity whose precise definition is given below. This continues author's earlier works, extending the boundedness range of to any triple of indices within the Banach triangle. Our result is optimal up to end-points.

Cite this article

Victor Lie, On the boundedness of the bilinear Hilbert transform along “non-flat” smooth curves. The Banach triangle case . Rev. Mat. Iberoam. 34 (2018), no. 1, pp. 331–353

DOI 10.4171/RMI/987