Banach-Valued Multilinear Singular Integrals with Modulation Invariance
We prove that the class of trilinear multiplier forms with singularity over a one-dimensional subspace, including the bilinear Hilbert transform, admits bounded L p-extension to triples of intermediate operatorname UMD spaces. No other assumption, for instance of Rademacher maximal function type, is made on the triple of UMD spaces. Among the novelties in our analysis is an extension of the phase-