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

  • Giancarlo Mauceri

    Università di Genova, Italy
  • Stefano Meda

    Università degli Studi di Milano-Bicocca, Italy
  • Peter Sjögren

    Chalmers University of Technology, Göteborg, Sweden

Abstract

In the setting of Euclidean space with the Gaussian measure , 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 , for . We determine which of them are bounded from to and from to BMO(). Here and BMO() 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.

Cite this article

Giancarlo Mauceri, Stefano Meda, Peter Sjögren, Endpoint estimates for first-order Riesz transforms associated to the Ornstein–Uhlenbeck operator. Rev. Mat. Iberoam. 28 (2012), no. 1, pp. 77–91

DOI 10.4171/RMI/667