A weighted decoupling inequality and its application to the maximal Bochner-Riesz problem

Abstract

We prove some weighted $L^p{\ell }^p$-decoupling estimates when $p=2n/(n-1)$. As an application, we give a result beyond the real interpolation exponents for the maximal Bochner-Riesz operator in $R^3$. We also make an improvement in the planar case.