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Pointwise smoothness, two-microlocalization and wavelet coefficients. (English) Zbl 0760.42016
The author discusses three notions of pointwise smoothness. He examines in detail pointwise smoothness and two-microlocalization, wavelet coefficients and J. M. Bony’s two-microlocal spaces $$C^{s,s'}_{x_ 0}$$, pseudodifferential operators and two-microlocalization and obtains several results.

##### MSC:
 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 46E15 Banach spaces of continuous, differentiable or analytic functions 46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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