The Convergence of Calder¨®n Reproducing Formulae of Two Parameters in $L^p$, in $\mathscr S$ and in $\mathscr S'$

Jiang-Wei Huang and Kunchuan Wang

Journal of Mathematics Research, 2017, vol. 9, issue 4, 87-100

Abstract: The Calder\'{o}n reproducing formula is the most important in the study of harmonic analysis, which has the same property as the one of approximate identity in many special function spaces. In this note, we use the idea of separation variables and atomic decomposition to extend single parameter to two-parameters and discuss the convergence of Calder\'{o}n reproducing formulae of two-parameters in $L^p(\mathbb R^{n_1} \times \mathbb R^{n_2})$, in $\mathscr S(\mathbb R^{n_1} \times \mathbb R^{n_2})$ and in $\mathscr S'(\mathbb R^{n_1} \times \mathbb R^{n_2})$.

Keywords: atomic decomposition; Calder\'on reproducing formula; Littlewood-Paley; Plancherel-P\^olya inequality (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:87-100

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