Lorentz Spaces
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Recent papers in Lorentz Spaces
It is well known that classical Sobolev's embeddings may be improved within the framework of Lorentz spaces. However, the value of the best possible constants in the corresponding inequalities is known in just one case by the work of A.... more
It is well known that classical Sobolev's embeddings may be improved within the framework of Lorentz spaces. However, the value of the best possible constants in the corresponding inequalities is known in just one case by the work of A. Alvino. Here, we determine optimal constants for the embedding of the space D 1,p (R n), 1 < p < n, into the whole Lorentz space scale L p * ,q (R n), p ≤ q ≤ ∞; including the case of Alvino q = p of which we give a new proof. We finally exhibit extremal functions for the embedding inequalities by solving related elliptic problems.
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