Riesz transforms for Jacobi expansions

Artikel i vetenskaplig tidskrift, 2008

We define Riesz transforms and conjugate Poisson integrals associated with multi-dimensional Jacobi expansions. Under a slight restriction on the type parameters, we prove that these operators are bounded in L p , 1 < p < ∞, with constants independent of the dimension. Our tools are suitably defined g-functions and Littlewood-Paley-Stein theory, involving the Jacobi-Poisson semigroup and modifications of it. © 2008 Springer Science+Business Media, Inc.