A sparse estimate for multisublinear forms involving vector-valued maximal functions
arXiv:1709.09647
Abstract
We prove a sparse bound for the -sublinear form associated to vector-valued maximal functions of Fefferman-Stein type. As a consequence, we show that the sparse bounds of multisublinear operators are preserved via -valued extension. This observation is in turn used to deduce vector-valued, multilinear weighted norm inequalities for multisublinear operators obeying sparse bounds, which are out of reach for the extrapolation theory recently developed by Cruz-Uribe and Martell. As an example, vector-valued multilinear weighted inequalities for bilinear Hilbert transforms are deduced from the scalar sparse domination theorem of the authors.
Submitted, Proceedings of the Bruno Pini Mathematical Analysis Seminar 2017