Bounds on the Norms of Maximal Operators on Weyl Sums
Roger C. Baker, Changhao Chen, Igor E. Shparlinski
TL;DR
This paper derives new optimal bounds for the maximal operator on Weyl sums, including detailed analysis of the quadratic case, using a novel combination of recent mathematical techniques.
Contribution
It introduces improved estimates for the maximal operator on Weyl sums, extending to quadratic cases with optimal bounds matching known lower bounds.
Findings
Optimal bounds for maximal operators on Weyl sums
Detailed analysis of quadratic (Gauss) sums
Estimates match lower bounds in wide parameter ranges
Abstract
We obtain new estimates on the maximal operator applied to the Weyl sums. We also consider the quadratic case (that is, Gauss sums) in more details. In wide ranges of parameters our estimates are optimal and match lower bounds. Our approach is based on a combination of ideas of Baker (2021) and Chen and Shparlinski (2020).
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Spectral Theory in Mathematical Physics · Mathematical Analysis and Transform Methods