16 Result(s)
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Article
Oscar Ciaurri
Mathematics
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Article
Discrete Harmonic Analysis Associated with Jacobi Expansions II: the Riesz Transform
The present work is the continuation of our study (Arenas et al. J. Math. Anal. Appl. 490(123996), 21, 2020) on discrete harmonic analysis related to Jacobi expansions. The role of a Laplacian is played by the op...
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Open AccessWeighted Transplantation for Laguerre Coefficients
We present a transplantation theorem for Laguerre coefficients in weighted spaces by means of a discrete local Calderón–Zygmund theory.
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Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
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 associated maximal operator and it...
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Bernoulli–Dunkl and Euler–Dunkl polynomials and their generalizations
Bernoulli–Dunkl and Euler–Dunkl polynomials are generalizations of the classical Bernoulli and Euler polynomials, using the Dunkl operator instead of the differential operator. In this paper, we study properti...
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Hardy’s inequality for the fractional powers of a discrete Laplacian
We prove a Hardy inequality for fractional powers of a discrete Laplacian, which can be seen as a generalized fractional version of the classical Hardy inequality in Landau (J Lond Math Soc 1:38–39, 1926). Such ...
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A Hardy Inequality for Ultraspherical Expansions with an Application to the Sphere
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 expansions. Our result also impl...
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Harmonic analysis associated with a discrete Laplacian
It is well known that the fundamental solution of $${u_t}\left( {n,t} \right) = u\left( {n + 1,t} \right) - 2u\left( {n,t} \right) + u...
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Riesz Transforms on Compact Riemannian Symmetric Spaces of Rank One
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 closely related to the Riesz trans...
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The Riesz Transform for the Harmonic Oscillator in Spherical Coordinates
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, we need a weighted inequal...
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The Poisson Operator for Orthogonal Polynomials in the Multidimensional Ball
In this paper we define the Poisson operator related to an orthonormal system on the multidimensional ball and we analyze some weighted inequalities for this operator in mixed norm spaces.
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The spectrum of the right inverse of the Dunkl operator
From the Dunkl analogue of Gegenbauer’s expansion of the plane wave, we derive an explicit closed formula for the spectrum of a right inverse of the Dunkl operator. This is done by stating the problem in such ...
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Higher Order Riesz Transforms for Fourier-Bessel Expansions
In this paper we investigate the Riesz transforms of order d≥1, \({\mathcal{R}}_{\nu}^{d}\) , for Fourier-Bessel expansi...
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Jacobi transplantation revisited
A transplantation theorem for Jacobi series proved by Muckenhoupt is reinvestigated by means of a suitable variant of Calderón–Zygmund operator theory. An essential novelty of our paper is weak type (1,1) esti...
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Weighted transplantation for Fourier-Bessel series
We prove weighted transplantation inequalities for Fourier-Bessel series with weights more general than previously considered power weights. These inequalities follow by using a local version of the Calderón-Z...
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Heat and Poisson Semigroups for Fourier-Neumann Expansions
Given \(\alpha > -1,\) consider the second order differential operator in
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A transference theorem for hermite expansions
A transference theorem for multipliers of Hermite expansions is proved. The result allows to transfer weightedL 2(ℝ n ) estimates from lower to higher dimensions.
