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Optimal Sobolev embeddings. (English) Zbl 0964.46012

Krbec, Miroslav (ed.) et al., Nonlinear analysis, function spaces and applications. Vol. 6. Proceedings of the spring school held in Prague, Czech Republic, May 31-June 6, 1998. Prague: Czech Academy of Sciences, Mathematical Institute. 156-199 (1999).
The author discusses the question when Sobolev type inequalities are optimal within various classes of function spaces. Sobolev spaces are modelled upon different scales of function spaces (e.g.Lebesgue, Orlicz, Lorentz, Lorentz-Zygmund, or rearrangement-invariant Banach function spaces) and a special attention is paid to embeddings in limiting situations. Quite general results are derived and the author applies them to concrete situations when Sobolev spaces are considered upon a given scale of function spaces.
For the entire collection see [Zbl 0952.00033].
Reviewer: B.Opic (Praha)

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47G10 Integral operators
26D10 Inequalities involving derivatives and differential and integral operators
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