2010
DOI: 10.1007/s11859-010-0684-9
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Characterizations of L p (R) using tight wavelet frames

Abstract: In this paper, a Littlewood-Paley function characterization of the spaces ( ), 1 ,is first established by means of the equivalent conditions of tight wavelet frames, wherein the Littlewood-Paley function is associated with a tight wavelet frame generated by the so-called extension principles. With the above characterization, another characterization of ( ), 1 , p L p ∞ R ∧ ∧ is also established in terms of the weighted 2 l -norm of the wavelet frame coefficients, which can be a useful tool in harmonic analysis… Show more

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Cited by 13 publications
(13 citation statements)
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“…Relative densities of Zn-modified samples are all above 90% and increase with the content of ZnO. The radius of Zn 2+ , Zr 4+ , Ce 4+ and O 2are 0.074nm, 0.072nm, 0.087nm and 0.140nm, respectively [17]. The ratio of r Zr to r O is 0.53.…”
Section: Resultsmentioning
confidence: 91%
“…Relative densities of Zn-modified samples are all above 90% and increase with the content of ZnO. The radius of Zn 2+ , Zr 4+ , Ce 4+ and O 2are 0.074nm, 0.072nm, 0.087nm and 0.140nm, respectively [17]. The ratio of r Zr to r O is 0.53.…”
Section: Resultsmentioning
confidence: 91%
“…As discussed above, the reaction of diazide and internal diyne meets the n th‐order model, which shows a near second‐order reaction characteristic. In our previous study, the kinetics of diazide and two terminal diynes was studied ; the E α of diazide and internal diyne is a little higher than those of diazide and terminal diynes because of maybe larger steric hindrance of internal diyne or a different reaction mechanism. For diazide and terminal diynes, the reactions are both first‐order reactions, which indicates that the reaction between diazide and internal diyne, diazide, and terminal diyne possesses different mechanisms.…”
Section: Resultsmentioning
confidence: 99%
“…On the contrary, the statistics showed that the B3LYP hybrid functional is superior to other forms of functional groups in many aspects. The estimation and calculation of the thermochemical properties of small and medium-sized systems are in the developing stage . C–S BDEs of small fragments were calculated, which revealed that the bond strength ranked as [C ar –S]–S–C ar > C ar –[S–S]–C ar > [C ar –S], and they were all proved by the experimental data.…”
Section: Introductionmentioning
confidence: 84%