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Discrete Harmonic Analysis associated with Jacobi expansions III: the Littlewood-Paley-Stein -functions and the Laplace type multipliers
Alberto Arenas, Óscar Ciaurri, Edgar Labarga
The research about Harmonic Analysis associated with Jacobi expansions carried out in \cite{ACL-JacI} and \cite{ACL-JacII} is continued in this paper. Given the operator $\mathcal{…
The convergence of discrete Fourier-Jacobi series
Alberto Arenas, Óscar Ciaurri, Edgar Labarga
The discrete counterpart of the problem related to the convergence of the Fourier-Jacobi series is studied. To this end, given a sequence, we construct the analogue of the partial…
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…
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…