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arXiv · 1906.07999

Discrete Harmonic Analysis associated with Jacobi expansions III: the Littlewood-Paley-Stein $g_{k}$-functions and the Laplace type multipliers

Alberto Arenas·Óscar Ciaurri·Edgar Labarga
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Abstract

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 $\mathcal{J}^{(\alpha,\beta)}=J^{(\alpha,\beta)}-I$, where $J^{(\alpha,\beta)}$ is the three-term recurrence relation for the normalized Jacobi polynomials and $I$ is the identity operator, we define the corresponding Littlewood-Paley-Stein $g_k^{(\alpha,\beta)}$-functions associated with it and we prove an equivalence of norms with weights for them. As a consequence, we deduce a result for Laplace type multipliers.

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Alberto Arenas, Óscar Ciaurri, Edgar Labarga. 2019-06-19. Discrete Harmonic Analysis associated with Jacobi expansions III: the Littlewood-Paley-Stein $g_{k}$-functions and the Laplace type multipliers. https://arxiv.org/abs/1906.07999

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