Resumen de Bounds for discrete multilinear spherical maximal functions

Theresa C. Anderson, Eyvindur Palsson

• We define a discrete version of the bilinear spherical maximal function, and show bilinear lp(Zd)×lq(Zd)→lr(Zd) bounds for d≥3, 1p+1q≥1r, r>dd−2 and p,q≥1. Due to interpolation, the key estimate is an lp(Zd)×l∞(Zd)→lp(Zd) bound, which holds when d≥3, p>dd−2. A key feature of our argument is the use of the circle method which allows us to decouple the dimension from the number of functions compared to the work of Cook.