Local estimates and global continuities in Lebesgue spaces for bilinear operators

Frederic Bernicot (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: Local estimates; multilinear operators; time-frequency analysis

Domaines: Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]

Frederic Bernicot. Local estimates and global continuities in Lebesgue spaces for bilinear operators. Analysis & PDE, 2008, 1, pp.1-27. ⟨hal-00218274v3⟩