Spaces of Besov-Sobolev type and a problem on nonlinear approximation
Journal of Functional Analysis(2023)
摘要
We study fractional variants of the quasi-norms introduced by Brezis, Van Schaftingen, and Yung in the study of the Sobolev space W˙1,p. The resulting spaces are identified as a special class of real interpolation spaces of Sobolev-Slobodeckiĭ spaces. We establish the equivalence between Fourier analytic definitions and definitions via difference operators acting on measurable functions. We prove various new results on embeddings and non-embeddings, and give applications to harmonic and caloric extensions. For suitable wavelet bases we obtain a characterization of the approximation spaces for best n-term approximation from a wavelet basis via smoothness conditions on the function; this extends a classical result by DeVore, Jawerth and Popov.
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关键词
46E35,26A33,26D10,35J05,35K05,39B22,42B35,46B70,46E30
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