Geodesic
Besov-type spaces and differences
Eurasian mathematical journal, Tome 11 (2020) no. 1, pp. 25-56

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We study characterizations by differences of the Besov-type spaces $B_{p,q}^{s,\tau}(\mathbb{R}^d)$. Our focus is on necessary and sufficient conditions on s for the validity of those characterizations. 
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     author = {M. Hovemann and W. Sickel},
     title = {Besov-type spaces and differences},
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M. Hovemann; W. Sickel. Besov-type spaces and differences. Eurasian mathematical journal, Tome 11 (2020) no. 1, pp. 25-56. http://geodesic.mathdoc.fr/item/EMJ_2020_11_1_a3/