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arXiv · 1709.09647

A sparse estimate for multisublinear forms involving vector-valued maximal functions

Amalia Culiuc·Francesco Di Plinio·Yumeng Ou
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Abstract

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 $\ell^r$-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.

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Amalia Culiuc, Francesco Di Plinio, Yumeng Ou. 2017-09-27. A sparse estimate for multisublinear forms involving vector-valued maximal functions. https://arxiv.org/abs/1709.09647

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