Two quantitative versions of the Nonlinear Carleson Conjecture

2025/05/11 by Sergey A. Denisov, Denisov, Sergey A.
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2505.06788

openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note compares two quantitative versions of the Nonlinear Carleson Conjecture (NCC). We provide motivations for our conjectures and show that they both imply the NCC. We discuss the connection to Carleson-Hunt maximal functions and give an SU(1,1) version of Calderon's theorem.

Citations

• Quantum signal processing and nonlinear Fourier analysis
• Generalizations of Menchov-Rademacher theorem and existence of wave operators in Schrodinger evolution
• A variation norm Carleson theorem
• A counterexample to a multilinear endpoint question of Christ and Kiselev

Related

• Quantitative Carleson's conjecture for Ahlfors regular domains
• Generalizations of the Carleson-Hunt theorem I. The classical singularity case
• Nevanlinna counting function and Carleson function of analytic maps
• On Extrapolation of Carleson Measures
• Quantitative control on the Carleson ε-function determines regularity