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An embedding theorem for the Orlicz-Sobolev space W^1, A₀ (G), G Rⁿ, into a space of Orlicz-Lorentz type is established for any given Young function A. Such a space is shown to be the best possible among all rearrangement invariant spaces. A version of the theorem for anisotropic spaces is also exhibited. In particular, our results recover and provide a unified framework for various well-known Sobolev type embeddings, including the classical inequalities for the standard Sobolev space W^1, p₀ (G) by O'Neil and by Peetre (1 p< n), and by Brezis-Wainger and by Hansson (p=n).
Andrea Cianchi (Tue,) studied this question.
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