Bellman function for the estimates of Littlewood–Paley type and asymptotic estimates in the [formula omitted] problem

Abstract

We utilize the method of Bellman functions to derive new L p -estimates of Littlewood–Paley type involving p − 1 . Among the applications to singular integrals we improve the 2 ( p − 1 ) bounds for the Ahlfors–Beurling operator on L p ( C ) when p → ∞ . In addition, dimensionless estimates of Riesz transforms in the classical as well as in the Ornstein–Uhlenbeck setting are attained. To cite this article: O. Dragičević, A. Volberg, C. R. Acad. Sci. Paris, Ser. I 340 (2005).