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Ron Kerman, Lubo Pick

Optimal Sobolev imbeddings

The aim of this paper is to study Sobolev-type imbedding inequalities involving rearrangement-invariant Banach function norms. We establish the equivalence of a Sobolev imbedding to the boundedness of a certain weighted Hardy operator. This Hardy operator is then used to prove the existence of rearrangement-invariant norms that are optimal in the imbedding inequality. Our approach is to use the methods and principles of Interpolation Theory.

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 18, 07/2006
Pages: 535 - 570

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