Geodesic
Some new function spaces of variable smoothness
Sbornik. Mathematics, Tome 206 (2015) no. 6, pp. 849-891

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A new Besov space of variable smoothness is introduced on which the norm is defined in terms of difference relations. This space is shown to be the trace of a weighted Sobolev space with a weight in the corresponding Muckenhoupt class. Methods of nonlinear spline approximation are applied to derive an atomic decomposition theorem for functions in a Besov space of variable smoothness. A complete description of traces on the hyperplane of a Besov space of variable smoothness and of a weighted Besov space with a weight in the corresponding Muckenhoupt class is given. Bibliography: 27 titles.
Keywords: Muckenhoupt weights, weighted Sobolev spaces, weighted Besov spaces, Besov spaces of variable smoothness. 
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     author = {A. I. Tyulenev},
     title = {Some new function spaces of variable smoothness},
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     url = {http://geodesic.mathdoc.fr/item/SM_2015_206_6_a3/}
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A. I. Tyulenev. Some new function spaces of variable smoothness. Sbornik. Mathematics, Tome 206 (2015) no. 6, pp. 849-891. http://geodesic.mathdoc.fr/item/SM_2015_206_6_a3/