Quantitative Polynomial Wiener-Wintner Theorems

Abstract

We prove quantitative polynomial Wiener--Wintner theorems in a very general setup, including measure-preserving actions of nilpotent Lie groups. Our results apply both to ergodic averages and to averages with singular integral weights. The proof relies on the generalized polynomial Carleson theorem developed in the companion paper by van Doorn, Srivastava, and the authors.

v2: 29 pages, incorporated referee comments; v3: final version accepted for publication in Israel J. Math., incorporated minor revisions following second referee report