Quantitative Polynomial Wiener-Wintner Theorems

2026/01/31 by Lars Becker, Asgar Jamneshan, Christoph Thiele
#math.DS #math.CA

paper · pdf

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.

Citations

• A Hard-Analytic Proof of "Most" Polynomial Wiener-Wintner Theorems for Infinite Measure Spaces
• Carleson operators on doubling metric measure spaces
• Quadratic maps between non-abelian groups
• A blueprint for the formalization of Carleson's theorem on convergence of Fourier series
• Automatic continuity of Polynomial maps and cocycles
• Discrete Analogues in Harmonic Analysis: A Theorem of Stein-Wainger
• Polynomial and horizontally polynomial functions on Lie groups
• Variational truncations of singular integrals on spaces of homogeneous type
• Variation-norm and fluctuation estimates for ergodic bilinear averages
• The Polynomial Carleson Operator
• A variation norm Carleson theorem
• The (weak-L²) Boundedness of The Quadratic Carleson Operator
• Pointwise ergodic theorems for actions of groups

Related

• Uniformity in the polynomial Wiener-Wintner theorem
• On the Wiener-Wintner theorem for nilsequences
• A uniform nilsequence Wiener-Wintner theorem for bilinear ergodic\n averages
• A note on uniform convergence of Wiener-Wintner ergodic averages
• Wiener's lemma along primes and other subsequences