Vol. 1, No. 1, 2008

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Local estimates and global continuities in Lebesgue spaces for bilinear operators

Frédéric Bernicot

Vol. 1 (2008), No. 1, 1–27
Abstract

In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg uncertainty principle correspond to a description of “off-diagonal decay”. In addition they allow us to prove global continuities in Lebesgue spaces for bilinear operators with spatial dependent symbol.

Keywords
local estimate, multilinear operator, time-frequency analysis, off-diagonal estimate
Mathematical Subject Classification 2000
Primary: 42B15, 42A20, 42A99
Milestones
Received: 16 January 2008
Accepted: 30 May 2008
Published: 2 October 2008
Authors
Frédéric Bernicot
Laboratoire de Mathématiques, bât. 425
Université Paris-Sud
91405 Orsay Cedex
France
http://www.math.u-psud.fr/~bernicot