Sparse bounds for discrete singular Radon transforms
Volume 165 / 2021
Colloquium Mathematicum 165 (2021), 199-217
MSC: Primary 42B20; Secondary 42B15.
DOI: 10.4064/cm8296-8-2020
Published online: 21 December 2020
Abstract
We show that discrete singular Radon transforms along a certain class of polynomial mappings $P:\mathbb {Z}^d\to \mathbb {Z}^n$ satisfy sparse bounds. For $n=d=1$ we can handle all polynomials. In higher dimensions, we pose restrictions on the admissible polynomial mappings stemming from a combination of interacting geometric, analytic and number-theoretic obstacles.
