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Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups. (English) Zbl 1356.46026
Summary: We work with Besov spaces \(\mathbf{B}_{p, q}^{0, b}\) defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent \(b\). We characterize \(\mathbf{B}_{p, q}^{0, b}\) by means of Fourier-analytical decompositions, wavelets and semi-groups. We also compare those results with the well-known characterizations for classical Besov spaces \(B_{p, q}^s\).

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46M35 Abstract interpolation of topological vector spaces
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42B25 Maximal functions, Littlewood-Paley theory
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