Remarks on Littlewood–Paley Analysis

Ho, Kwok-Pun

Canadian journal of mathematics, Tome 60 (2008) no. 6, pp. 1283-1305

Résumé

Littlewood–Paley analysis is generalized in this article. We show that the compactness of the Fourier support imposed on the analyzing function can be removed. We also prove that the Littlewood–Paley decomposition of tempered distributions converges under a topology stronger than the weak-star topology, namely, the inductive limit topology. Finally, we construct a multiparameter Littlewood–Paley analysis and obtain the corresponding “renormalization” for the convergence of this multiparameter Littlewood–Paley analysis.

Détail

DOI : 10.4153/CJM-2008-055-x

Mots-clés : 42B25, Littlewood–Paley analysis, distributions

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