Sharp embeddings of Besov-type spaces

We prove sharp embeddings of Besov spaces B p , r σ , b ( R ) involving both the classical smoothness σ and a slowly varying smoothness b into Lorentz–Karamata spaces. Our methods are quite elementary, we use neither the interpolation theory nor the atomic decomposition of spaces in question. We cov...

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Veröffentlicht in:	Journal of computational and applied mathematics 2007-11, Vol.208 (1), p.235-269
Hauptverfasser:	Gurka, Petr, Opic, Bohumír
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximations and expansions Besov spaces with slowly varying smoothness Exact sciences and technology Functional analysis Growth envelope functions Growth envelopes Lorentz–Karamata spaces Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Sciences and techniques of general use Sharp embeddings
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Zusammenfassung:	We prove sharp embeddings of Besov spaces B p , r σ , b ( R ) involving both the classical smoothness σ and a slowly varying smoothness b into Lorentz–Karamata spaces. Our methods are quite elementary, we use neither the interpolation theory nor the atomic decomposition of spaces in question. We cover both sub-limiting and limiting cases and we determine growth envelopes of spaces B p , r σ , b ( R ) .
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2006.10.036