2-Microlocal Besov Spaces

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


We introduce 2-microlocal Besov spaces which generalize the 2-microlocal spaces \({C}_{{x}_{0}}^{s,s^{\prime}}(\mathbb{R}n)\) by Bony. We give a unified Fourier-analytic approach to define generalized 2-microlocal Besov spaces and we present a wavelet characterization for them. Wavelets provide a powerful tool for studying global and local regularity properties of functions. Further, we prove a characterization with wavelets for the local version of the 2-microlocal Besov spaces and we give first connections and generalizations to local regularity theory.


Besov Space Local Space Local Regularity Daubechies Wavelet Open Neighborhood Versus 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematical InstituteFriedrich Schiller UniversityJenaGermany

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