Wilfredo Urbina

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Abstract In this article we study the fractional Integral and the fractional Derivative for Jacobi expansion. In order to do that we obtain an analogous of P. A. Meyer’s Multipliers Theorem for Jacobi expansions. We also obtain a version of Calderón’s reproduction formula for the Jacobi measure. Finally, as an application of the fractional differentiation,(More)
In this paper we study the controllability of the following controlled Ornstein–Uhlenbeck equation z t = 1 2 z − −x, ∇z + ∞ n=1 |β|=n u β (t)b, h β γ d h β , t > 0, x ∈ R d , where h β is the normalized Hermite polynomial, b ∈ L 2 (γ d), γ d (x) = e −|x| 2 π d/2 is the Gaussian measure in R d and the control u ∈ L 2 (0, t 1 ; l 2 (γ d)), with l 2 (γ d) the(More)
We show pointwise estimates for the maximal operator of the Ornstein-Uhlenbeck semigroup for functions that are integrable with respect to the Gaussian measure. The estimates are used to prove pointwise convergence. The Ornstein-Uhlenbeck semigroup is defined by Ttf(x)= [ k(t,x,y)f(y)dy, Jr" where ,1. \ -"/2m -2f,-«/2 / \e~'x-y\ \ 4 ^ _ ^ D« k(t, x, y) n (1(More)
The purpose of this paper is to prove the L p (R n ; dd) boundedness, for p > 1, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure dd = e ?jxj 2 dx. Let dd = e ?jxj 2 dx be a Gaussian measure in Euclidean space R n. We consider the non-centered maximal function deened by Mf(x) = sup x2B 1 (B) Z B jfj dd; where the(More)
In this paper we are going to get the non tangential convergence, in an appropriated parabolic “gaussian cone”, of the Ornstein-Uhlenbeck semigroup in providing two proofs of this fact. One is a direct proof by using the truncated non tangential maximal function associated. The second one is obtained by using a general statement. This second proof also(More)
In this paper we define Besov-Lipschitz and Triebel-Lizorkin spaces in the context of Gaussian harmonic analysis, the harmonic analysis of Hermite polynomial expansions. We study inclusion relations among them, some interpolation results and continuity results of some important operators (the Ornstein-Uhlenbeck and the Poisson-Hermite semigroups and the(More)
In this paper we consider the Gaussian Besov-Lipschitz B α p,q (γ d) and Gaussian Triebel-Lizorkin F α p,q (γ d) spaces, for any α > 0, studying the inclusion relations among them, proving that the Gaussian Sobolev spaces L p α (γ d) are contained in them, giving some interpolation results and studying the continuity properties of the Ornstein-Uhlenbeck(More)
In this paper we consider the Gaussian Besov-Lipschitz B α p,q (γ d) and Gaussian Triebel-Lizorkin F α p,q (γ d) spaces, for any α > 0, studying the inclusion relations among them, proving that the Gaussian Sobolev spaces L p α (γ d) are contained in them, giving some interpolation results and studying the continuity properties of the Ornstein-Uhlenbeck(More)
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