Characterizations of Lp(R) using tight wavelet frames |
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Authors: | Dayong Lu Qibin Fan |
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Affiliation: | (2) Department of Mathematics, The University of Georgia, Athens, USA; |
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Abstract: | In this paper, a Littlewood-Paley function characterization of the spaces L p (R), 1 < p< ∞ 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 L p (R), 1 < p< ∞ is also established in terms of the weighted l 2-norm of the wavelet frame coefficients, which can be a useful tool in harmonic analysis, approximation theory, and image processing. |
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Keywords: | wavelet frames extension principles Littlewood-Paley functions the regularity class |
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