A linear dimensionless bound for the weighted Riesz vector

Komla Domelevo (1) , Stefanie Petermichl (1, 2) , Janine Wittwer (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IUF - Institut universitaire de France
3 Westminster College

We show that the norm of the vector of Riesz transforms as operator in the weighted Lebesgue space $L^2_ω$ is bounded by a constant multiple of the first power of the Poisson-$A_2$ characteristic of $ω$. The bound is free of dimension. We also show that for $n > 1$, the Poisson-$A_2$ class is properly included in the classical $A_2$ class.

Mots clés: Bellman function; Riesz transforms; weighted estimates

Domaines: Mathématiques [math]

Komla Domelevo, Stefanie Petermichl, Janine Wittwer. A linear dimensionless bound for the weighted Riesz vector. Bulletin des Sciences Mathématiques, 2017, 141 (5), pp.385-407. ⟨10.1016/j.bulsci.2017.05.004⟩. ⟨hal-01097113⟩