Print Email Facebook Twitter Multilinear transference of Fourier and Schur multipliers acting on non-commutative Lp-spaces Title Multilinear transference of Fourier and Schur multipliers acting on non-commutative Lp-spaces Author Caspers, M.P.T. (TU Delft Analysis) Krishnaswamy Usha, A. (TU Delft Analysis) Vos, G.M. (TU Delft Analysis) Date 2022 Abstract Let G be a locally compact unimodular group, and let φ be some function of n variables on G. To such a φ, one can associate a multilinear Fourier multiplier, which acts on some n-fold product of the noncommutative L p-spaces of the group von Neumann algebra. One may also define an associated Schur multiplier, which acts on an n-fold product of Schatten classes S p(L 2(G). We generalize well-known transference results from the linear case to the multilinear case. In particular, we show that the so-called multiplicatively bounded (p1,....,pn)-norm"of a multilinear Schur multiplier is bounded above by the corresponding multiplicatively bounded norm of the Fourier multiplier, with equality whenever the group is amenable. Furthermore, we prove that the bilinear Hilbert transform is not bounded as a vector-valued map L p1(R,S p1) × L p2 (R,S p2), → L 1(R,S 1), whenever p1 and p2 are such that {equation presented}. A similar result holds for certain Calderón-Zygmund-type operators. This is in contrast to the nonvector-valued Euclidean case. Subject Fourier multipliersmultilinear mapsnon-commutative LspacesSchur multipliers To reference this document use: http://resolver.tudelft.nl/uuid:b03097c3-26c1-4b3c-a968-aba9071e991b DOI https://doi.org/10.4153/S0008414X2200058X ISSN 0008-414X Source Canadian Journal of Mathematics, 75 (6), 1986-2006 Part of collection Institutional Repository Document type journal article Rights © 2022 M.P.T. Caspers, A. Krishnaswamy Usha, G.M. Vos Files PDF multilinear_transference_ ... spaces.pdf 614.95 KB Close viewer /islandora/object/uuid:b03097c3-26c1-4b3c-a968-aba9071e991b/datastream/OBJ/view