In the setting of Euclidean space with the Gaussian measure γ, 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), for 1 < p < ∞. We determine which of them are bounded from H1(γ) to L1(γ) and from L∞(γ) to BMO(γ). Here H1(γ) and BMO(γ) 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. © European Mathematical Society.
Mauceri, G., Meda, S., Sjogren, P. (2012). Endpoint estimates for first-order Riesz transforms associated to the Ornstein-Uhlenbeck operator. REVISTA MATEMATICA IBEROAMERICANA, 28(1), 77-91 [10.4171/RMI/667].
Endpoint estimates for first-order Riesz transforms associated to the Ornstein-Uhlenbeck operator
MEDA, STEFANO
Secondo
;
2012
Abstract
In the setting of Euclidean space with the Gaussian measure γ, 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), for 1 < p < ∞. We determine which of them are bounded from H1(γ) to L1(γ) and from L∞(γ) to BMO(γ). Here H1(γ) and BMO(γ) 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. © European Mathematical Society.
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