Multilinear Fourier multipliers related to time–frequency localization

Abstract

a b s t r a c tWe consider multilinear multipliers associated in a natural way with localization operators. Boundedness and compactness results are obtained. In particular, we get a geometric condition on a subset A ⊂ R 2d which guarantees that, for a fixed synthesis window ψ ∈ L 2 (R d ), the family of localization operators L A ϕ,ψ obtained when the analysis window ϕ varies on the unit ball of L 2 (R d ) is a relatively compact set of compact operators.