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Article
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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Article
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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Article
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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Article
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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Article
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...