Remarks on Littlewood--Paley Analysis

http://dx.doi.org/10.4153/CJM-2008-055-x
Canad. J. Math. 60(2008), 1283-1305

  Published:2008-12-01
 Printed: Dec 2008

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.