Bellman function for the estimates of Littlewood-Paley type and asymptotic estimates in the ▫$p-1$▫ problem
Dragičević, Oliver ; Volberg, Alexander
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 ▫$L^p(\mathbb C)$▫ when ▫$p \to \infty$▫. In addition, dimensionless estimates of Riesz transforms in the classical as well as in the Ornstein-Uhlenbeck setting are attained.
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