Sharp bounds for the distribution of martingale transforms of bounded functions
Abstract
The paper suggests a characterization of a positive function f f such that f ( ψ ∞ ) f(\psi _\infty ) is integrable for any limit value ψ ∞ \psi _\infty of the martingale transform for an indicator function. The characterizing condition is that a version of the Lipschitz majorant of f f is integrable with respect to an exponential weight. The arguments are based on the calculation of particular minimal biconcave functions on a strip.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Mathematical Dynamics and Fractals
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- St Petersburg Mathematical Journal
- Volume
- 36
- Issue
- 4
- Pages
- 545–605
- Publication date
- 6 January 2026
- Language
- EN