Banach-Valued Multilinear Singular Integrals with Modulation Invariance
Banach-Valued Multilinear Singular Integrals with Modulation Invariance
Abstract 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 $\operatorname{UMD}$ spaces. Among the …