Bounds for discrete multilinear spherical maximal functions

Anderson, Theresa C. ^[1] ; Palsson, Eyvindur Ari ^[2]
1. [1] Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN, 47907, USA
2. [2] Department of Mathematics, Virginia Tech, 225 Stanger St., Blacksburg, VA, 24061, USA
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 1, 2022, págs. 75-87
Idioma: inglés
DOI: 10.1007/s13348-020-00308-z
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Resumen
- 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.