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6 papers
Fractional moments
Óscar Ciaurri
We evaluate the moments of some functions composed with the fractional part of . We name them fractional moments. In particular, we obtain expressions for the fractional momen…
Discrete Harmonic Analysis associated with Jacobi expansions II: the Riesz transform
Alberto Arenas, Óscar Ciaurri, Edgar Labarga
This paper is the continuation of the study on discrete harmonic analysis related to Jacobi expansions initiated in [1]. Considering the operator ,…
A weighted transplantation theorem for Jacobi coefficients
Alberto Arenas, Óscar Ciaurri, Edgar Labarga
We present a transplantation theorem for Jacobi coefficients in weighted spaces. In fact, by using a discrete vector-valued local Calderón-Zygmund theory, which has recently been f…
Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
Óscar Ciaurri, Adam Nowak, Luz Roncal
We study a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associ…
Discrete harmonic analysis associated with Jacobi expansions I: the heat semigroup
Alberto Arenas, Óscar Ciaurri, Edgar Labarga
In this paper we commence the study of discrete harmonic analysis associated with Jacobi orthogonal polynomials of order . Particularly, we give the solution ,…
A Hardy inequality for ultraspherical expansions with an application to the sphere
Alberto Arenas, Óscar Ciaurri, Edgar Labarga
We prove a Hardy inequality for ultraspherical expansions by using a proper ground state representation. From this result we deduce some uncertainty principles for this kind of exp…