José L. Torrea

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We consider higher order Riesz transforms for the multi-dimensional Hermite function expansions. The Riesz transforms occur to be Calderón-Zygmund operators hence their mapping properties follow by using results from a general theory. Then we investigate higher order conjugate Poisson integrals showing that at the boundary they approach appropriate Riesz(More)
We develop a generalized Littlewood-Paley theory for semigroups acting on Lp-spaces of functions with values in uniformly convex or smooth Banach spaces. We characterize, in the vector-valued setting, the validity of the one-sided inequalities concerning the generalized Littlewood-PaleyStein g-function associated with a subordinated Poisson symmetric(More)
In the last few years several authors have been concerned with the harmonic analysis associated to the operator H (see for instance [5,10,12]). In this analysis the operators A j play the role of the partial derivative operators ∂/∂x j in the classical Euclidean case. Hence it seems natural to study the spaces of functions in Lp(Rd) whose derivatives also(More)
Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on Lp(IRd), 1 < p < ∞. In this paper we give a different proof that allows us to show that the Lp−norms of these operators are bounded by a constant not depending on the dimension d. Moreover, we define Riesz transforms of higher(More)
For each p in [1,∞) let Ep denote the closure of the region of holomorphy of the Ornstein–Uhlenbeck semigroup {Ht : t > 0} on L with respect to the Gaussian measure. Sharp weak type and strong type estimates are proved for the maximal operator f 7→ H∗pf = sup{|Hzf| : z ∈ Ep} and for a class of related operators. As a consequence, a new and simpler proof of(More)
A well known result by Rubio de Francia asserts that for every finite family of disjoint intervals {Ik} in R, and p in the range 2 ≤ p < ∞, there exists Cp > 0 such that ‖ X k rkSIkf‖Lp Lp([0,1])(R) ≤ Cp‖f‖Lp(R), where the rk’s are the Rademacher functions. In this note we prove that, given a compact connected abelian group G with dual group Γ and p in the(More)
A cost-effectiveness analysis was made to determine the effectiveness of the following strategies of mass immunization with the new recombinant vaccine against the hepatitis B virus in Spain: vaccination of adolescents, newborns, both populations, and vaccination plus passive immunization of newborns of HBsAg positive mothers. Decision trees supported on(More)
We prove weighted L-inequalities for the gradient square function associated with the Poisson semigroup in the multi-dimensional Hermite function expansions setting. In the proof a technique of vector valued Calderón-Zygmund operators is used. 2000 Mathematics Subject Classification. Primary 42C10; Secondary 42B20.