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 l^{p}(\mathbb {Z}^d)\times l^{q}(\mathbb {Z}^d) \rightarrow l^{r}(\mathbb {Z}^d) bounds for d \ge 3, \frac{1}{p} + \frac{1}{q} \ge \frac{1}{r}, r>\frac{d}{d-2} and p,q\ge 1. Due to interpolation, the key estimate is an l^{p}(\mathbb {Z}^d)\times l^{\infty }(\mathbb {Z}^d) \rightarrow l^{p}(\mathbb {Z}^d) bound, which holds when d \ge 3, p>\frac{d}{d-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.