On Calderón’s conjecture for the bilinear Hilbert transform
AUTOR(ES)
Lacey, Michael T.
FONTE
The National Academy of Sciences
RESUMO
We show that the bilinear Hilbert transform defined by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\boldsymbol{{\mathit{Hfg}}}(\boldsymbol{{\mathit{x}}})\boldsymbol{{\mathrm{\hspace{.167em}=\hspace{.167em}p.v.}}{\mathit{\hspace{.167em}}}}{\int }\boldsymbol{{\mathit{\hspace{.167em}f}}}(\boldsymbol{{\mathit{x\hspace{.167em}-\hspace{.167em}y}}})\boldsymbol{{\mathit{g}}}(\boldsymbol{{\mathit{x\hspace{.167em}+\hspace{.167em}y}}})\boldsymbol{{\mathit{\hspace{.167em}}}}\frac{\boldsymbol{{\mathit{dy}}}}{\boldsymbol{{\mathit{y}}}}\end{equation*}\end{document} maps Lp × Lq into Lrfor 1 < p, q ≤ ∞, 1/p + 1/q = 1/r, and 2/3 < r < ∞.
ACESSO AO ARTIGO
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=20172Documentos Relacionados
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