Local estimates and global continuities in Lebesgue spaces for bilinear operators

Bernicot, Frédéric

doi:10.2140/apde.2008.1.1

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Local estimates and global continuities in Lebesgue spaces for bilinear operators

Frédéric Bernicot

Vol. 1 (2008), No. 1, 1–27

DOI: 10.2140/apde.2008.1.1

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

Vol. 1, No. 1, 2008