Lp estimates for the bilinear Hilbert transform

AUTOR(ES)

Lacey, Michael

FONTE

The National Academy of Sciences of the USA

RESUMO

For the bilinear Hilbert transform given by: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathit{H\hspace{.167em}fg}}({\mathit{x}}){\mathrm{\hspace{.167em}=\hspace{.167em}p.v.}}{\int }{\mathit{f}}({\mathit{x\hspace{.167em}-\hspace{.167em}y}}){\mathit{g}}({\mathit{x\hspace{.167em}+\hspace{.167em}y}}){\mathrm{\hspace{.167em}}}\frac{{\mathit{dy}}}{{\mathit{y}}}{\mathrm{,}}\end{equation*}\end{document} we announce the inequality ∥H fg∥p3 ≤ Kp1,p2∥f∥p1∥g∥p2, provided 2 < p1, p2 < ∞, 1/p3 = 1/p1 + 1/p2 and 1 < p3 < 2.

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