85 citations · 176 across the 22 of their papers we have counts for
25 papers
Uniform weighted inequalities for the Hankel transform transplantation operator
Óscar Ciaurri
In this paper we present uniform weighted inequalities for the Hankel transform transplantation operator. A weighted vector-valued inequality is also obtained. As a consequence we…
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 ,…
Fourier Series of Gegenbauer-Sobolev Polynomials
Óscar Ciaurri, Judit Mínguez
We study the partial sum operator for a Sobolev-type inner product related to the classical Gegenbauer polynomials. A complete characterization of the partial sum operator in an ap…
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…
Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions
Óscar Ciaurri, Adam Nowak, Luz Roncal
We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this…
Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions
Óscar Ciaurri, Antonio J. Durán, Mario Pérez +1
We introduce Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials as generalizations of Bernoulli and Apostol-Euler polynomials, where the role of the derivative is now played by th…
Hardy-type inequalities for fractional powers of the Dunkl--Hermite operator
Ó. Ciaurri, L. Roncal, S. Thangavelu
We prove Hardy-type inequalities for a fractional Dunkl--Hermite operator which incidentally give Hardy inequalities for the fractional harmonic oscillator as well. The idea is to…
Revisiting floating bodies
Óscar Ciaurri, Emilio Fernández, L. Roncal
The conic sections, as well as the solids obtained by revolving these curves, and many of their surprising properties, were already studied by Greek mathematicians since at least t…
Unconditional and quasi-greedy bases in with applications to Jacobi polynomials Fourier series
Fernando Albiac, José L. Ansorena, Óscar Ciaurri +1
We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in does not converge unless . As a by-product of our…
Fractional discrete Laplacian versus discretized fractional Laplacian
Ó. Ciaurri, L. Roncal, P. R. Stinga +2
We define and study some properties of the fractional powers of the discrete Laplacian for and . A comparison b…
Harmonic Analysis associated with a discrete Laplacian
Ó. Ciaurri, T. A. Gillespie, L. Roncal +2
It is well-known that the fundamental solution of with for every fixed , is given…
Fourier--Jacobi expansions in Morrey spaces
A. Arenas, Ó. Ciaurri
In this paper we obtain a characterization of the convergence of the partial sum operator related to Fourier--Jacobi expansions in Morrey spaces.
Riesz transforms on compact Riemannian symmetric spaces of rank one
Ó. Ciaurri, L. Roncal, P. R. Stinga
In this paper we prove mixed norm estimates for Riesz transforms related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. These operators are clos…
The Riesz transform for the harmonic oscillator in spherical coordinates
Ó. Ciaurri, L. Roncal
In this paper we show weighted estimates in mixed norm spaces for the Riesz transform associated with the harmonic oscillator in spherical coordinates. In order to prove the result…
Vector-valued extensions for fractional integrals of Laguerre expansions
Ó. Ciaurri, L. Roncal
We prove some vector-valued inequalities for fractional integrals defined in the context of two different orthonormal systems of Laguerre functions. Our results are based on estima…
A -linear analogue of the plane wave expansion
Luís Daniel Abreu, Óscar Ciaurri, Juan Luis Varona
We obtain a -linear analogue of Gegenbauer's expansion of the plane wave. It is expanded in terms of the little -Gegenbauer polynomials and the \textit{third} Jackson -Bes…
A simple computation of by using Bernoulli polynomials and a telescoping series
Ó. Ciaurri, L. M. Navas, F. J. Ruiz +1
We present a new proof of Euler's formulas for , where , which uses only the defining properties of the Bernoulli polynomials, obtaining the value of …
Fractional integrals on compact Riemannian symmetric spaces of rank one
O. Ciaurri, L. Roncal, P. R. Stinga
In this paper we study mixed norm boundedness for fractional integrals related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. The key point is t…
Mean convergence of Fourier-Dunkl series
Ó. Ciaurri, M. Pérez, J. M. Reyes +1
In the context of the Dunkl transform a complete orthogonal system arises in a very natural way. This paper studies the weighted norm convergence of the Fourier series expansion as…
Bilinear biorthogonal expansions and the Dunkl kernel on the real line
L. D. Abreu, Ó. Ciaurri, J. L. Varona
We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structu…