We give a characterization of the two-microlocal Besov spaces in terms of the local Besov type conditions. As an easy consequence, we obtain the inclusions between the two-microlocal Besov spaces and the local Besov spaces. These results are natural extensions of those obtained by Jaffard and Meyer, who treated the pointwise H\"older regularity in terms of two-microlocal estimates. The Daubechies wavelets play a key role throughout the paper.
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Shinya Moritoh, Tomomi Yamada, Two–microlocal Besov spaces and wavelets. Rev. Mat. Iberoam. 20 (2004), no. 1, pp. 277–283DOI 10.4171/RMI/389