Wavelet transforms and operators in various function spaces

Shinya Moritoh ()
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Shinya Moritoh: Nara Women’s University, Department of Mathematics

A chapter in New Trends in Microlocal Analysis, 1997, pp 59-68 from Springer

Abstract: Abstract We define a class of wavelet transforms as a continuous and micro-local version of the Littlewood-Paley decompositions. Hörmander’s wave front sets (see [3]) as well as the Besov and Triebel-Lizorkin spaces (see [6] and [7]) may be characterized in terms of our wavelet transforms. By using the results obtained above (see [4]), we characterize the wave front sets in the sense of the Besov-Triebel-Lizorkin regularity in terms of our wavelet transforms. Finally, Päivärinta’s results on the continuity of pseudodifferential operators in the Besov-Triebel-Lizorkin spaces (see [9]) may be microlocalized. In other words, we show the pseudo-microlocal properties in the sense of the Besov-Triebel-Lizorkin regularity. We remark that the components of our decompositions are not linearly independent but can be treated as if they were.

Keywords: Function Space; Besov Space; Pseudodifferential Operator; Inverse Fourier Transform; Inversion Formula (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68413-8_4

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DOI: 10.1007/978-4-431-68413-8_4

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