Sparse bounds for the bilinear spherical maximal function

Abstract

We derive sparse bounds for the bilinear spherical maximal function in any dimension d ≥ 2. This immediately recovers the sharp L p × L q → L r bound of the operator and implies quantitative weighted norm inequalities with respect to bilinear Muckenhoupt weights, which seems to be the first of their kind for the operator. The key innovation is a group of newly developed continuity L p improving estimates for the localized version of the bilinear spherical maximal function.

The Multilinear Spherical Maximal Function in one dimension

“…This was generalized to the multilinear setting in [11]. See also [1], [2], [12], and [7] for further developments.…”