We prove a sparse bound for the m-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 ℓr-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 developed by Cruz-Uribe and Martell in Limited range multilinear extrapolation with applications to the bilinear Hilbert transform, preprint arXiv:1704.06833 (2017). As an example, vector-valued multilinear weighted inequalities for bilinear Hilbert transforms are deduced from the scalar sparse domination theorem of Domination of multilinear singular integrals by positive sparse forms, preprint arXiv:1603.05317.
@article{8171,
title = {A Sparse Estimate for Multisublinear Forms Involving Vector-valued Maximal Functions},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2018},
doi = {10.6092/issn.2240-2829/8171},
language = {EN},
url = {http://dml.mathdoc.fr/item/8171}
}
Culiuc, Amalia; Di Plinio, Francesco; Ou, Yumeng. A Sparse Estimate for Multisublinear Forms Involving Vector-valued Maximal Functions. Bruno Pini Mathematical Analysis Seminar, (2018), . doi : 10.6092/issn.2240-2829/8171. http://gdmltest.u-ga.fr/item/8171/