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Wavelet transforms in Euclidean spaces – their relation with wave front sets and Besov, Triebel-Lizorkin spaces. (English) Zbl 0843.35146

Summary: We define a class of wavelet transforms as a continuous and microlocal version of the Littlewood-Paley decompositions. Hörmander’s wave front sets as well as the Besov and Triebel-Lizorkin spaces may be characterized in terms of our wavelet transforms.

MSC:

35S30 Fourier integral operators applied to PDEs
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42B25 Maximal functions, Littlewood-Paley theory
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References:

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