Endpoint estimates for first-order Riesz transforms associated to the Ornstein-Uhlenbeck operator

Original · EN

In the setting of Euclidean space with the Gaussian measure g, we consider all first-order Riesz transforms associated to the infinitesimal generator of the Ornstein-Uhlenbeck semigroup. These operators are known to be bounded on Lᵖ(g), for 1<p<∞. We determine which of them are bounded from H¹(g) to L¹(g) and from L∞(g) to BMO(g). Here H¹(g) and BMO(g) are the spaces introduced in this setting by the first two authors. Surprisingly, we find that the results depend on the dimension of the ambient space.