Remarks on Littlewood-Paley analysis

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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. Copyright © 2008 Canadian Mathematical Society.
Original languageEnglish
Pages (from-to)1283-1305
JournalCanadian Journal of Mathematics
Issue number6
Publication statusPublished - 01 Dec 2008


Ho, K.-P. (2008). Remarks on Littlewood-Paley analysis. Canadian Journal of Mathematics, 60(6), 1283-1305. doi: 10.4153/CJM-2008-055-x


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