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DOE OSTI · 22590455

Some new function spaces of variable smoothness

Tyulenev, A I
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Abstract

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.

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97 MATHEMATICS AND COMPUTINGMANY-DIMENSIONAL CALCULATIONSMATHEMATICAL SPACESMOOTH MANIFOLDS

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BibTeXRIS

Tyulenev, A I. 2015-06-30. Some new function spaces of variable smoothness. https://doi.org/10.1070/sm2015v206n06abeh004481

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