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A sharp embedding theorem for Orlicz-Sobolev spaces. (English) Zbl 0860.46022

With any Young function \(A\) it is associated a Young function \(B\) having the property that, for any sufficiently smooth subset \(G\) of \(\mathbb{R}^n\), \(L^B(G)\) is the smallest Orlicz space into which the Orlicz-Sobolev space \(W^{1,A}(G)\) is continuously embedded.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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