Mixed norm Leibnitz rules via multilinear operator valued multipliers

Analysis Seminar
Thursday, November 19, 2015 - 4:35pm
1 hour (actually 50 minutes)
Skiles 006
Brown University
[Special time and location] The content of this talk is joint work with Yumeng Ou. We describe a novel framework for the he analysis of multilinear singular integrals acting on Banach-valued functions.Our main result is a Coifman-Meyer type theorem for operator-valued multilinear multipliers acting on suitable tuples of UMD spaces, including, in particular, noncommutative Lp spaces. A concrete case of our result is a multilinear generalization of Weis' operator-valued Hormander-Mihlin linear multiplier theorem.Furthermore, we derive from our main result a wide range of mixed Lp-norm estimates for multi-parameter multilinear multiplier operators, as well as for the more singular tensor products of a one-parameter Coifman-Meyer multiplier with a bilinear Hilbert transform. These respectively extend the results of Muscalu et. al. and of Silva to the mixed norm case and provide new mixed norm fractional Leibnitz rules.