Multilinear maximal operators associated to simplices

Abstract

We prove ℓ p 1 × • • • × ℓ p k → ℓ r bounds for multilinear maximal operators associated to averages over all isometric copies of a given non-degenerate k-simplex. This provides a natural extension of ℓ p → ℓ p bounds for the discrete spherical maximal operator, which also serves as the key ingredient of our proof.