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# Remarks on Littlewood--Paley Analysis

Published:2008-12-01
Printed: Dec 2008
• Kwok-Pun Ho
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## Abstract

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.
 Keywords: Littlewood--Paley analysis, distributions
 MSC Classifications: 42B25 - Maximal functions, Littlewood-Paley theory

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