JournalsrmiVol. 28, No. 1pp. 77–91

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

In the setting of Euclidean space with the Gaussian measure γ\gamma, 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(γ)L^p(\gamma), for 1<p<1< p< \infty. We determine which of them are bounded from H1(γ)H^1(\gamma) to L1(γ)L^1(\gamma) and from L(v)L^\infty(v) to BMO(γ\gamma). Here H1(γ)H^1(\gamma) and BMO(γ\gamma) 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