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

Primary: 42B15, 42A20, 42A99

Authors