Two quantitative versions of the Nonlinear Carleson Conjecture
Sergey A. Denisov
TL;DR
This paper compares two quantitative forms of the Nonlinear Carleson Conjecture, demonstrating their implications for the original conjecture and exploring connections to maximal functions and harmonic analysis theorems.
Contribution
It introduces and analyzes two new quantitative versions of the NCC, showing their equivalence and implications for harmonic analysis.
Findings
Both versions imply the NCC.
Connections established to Carleson-Hunt maximal functions.
An SU(1,1) version of Calderon's theorem is provided.
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.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Banach Space Theory · Nonlinear Partial Differential Equations