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On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves

Classical Analysis and ODEs 2016-01-05 v2
Authors: Victor Lie
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Abstract

We are proving L2(R)×L2(R) → L1(R)L^2(\R)\times L^2(\R)\,\rightarrow\,L^1(\R) bounds for the bilinear Hilbert transform HΓH_{\Gamma} along curves Γ=(t,−γ(t))\Gamma=(t,-\gamma(t)) with γ\gamma being a smooth "non-flat" curve near zero and infinity.

Keywords

bilinear Hilbert transform non-flat smooth curves L^2 to L^1 boundedness singular integrals time-frequency analysis

Cite

@article{arxiv.1110.3517,
  title  = {On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves},
  author = {Victor Lie},
  journal= {arXiv preprint arXiv:1110.3517},
  year   = {2016}
}

Comments

48 pages, no figures. Published in Amer. J. Math., 137(2), pp. 313-364, 2015

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