Multi-linear multipliers associated to simplexes of arbitrary length

Muscalu, Camil; Tao, Terence; Thiele, Christoph

Multi-linear multipliers associated to simplexes of arbitrary length

Authors

Muscalu, Camil

Tao, Terence

Thiele, Christoph

Description

In this article we prove that the $n$-linear operator whose symbol is the characteristic function of the simplex $Δ_n = ξ_1 < ... < ξ_n$ is bounded from $L^2 \times ... \times L^2$ into $L^{2/n}$, generalizing in this way our previous work on the "bi-est" operator (which corresponds to the case $n=3$) as well as Lacey-Thiele theorem on the bi-linear Hilbert transform (which corresponds to the case $n=2$).
52 pages, 6 figures