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Best Remainder Norms in Sobolev-Hardy Inequalities

We exhibit the optimal norm for a remainder term in the sharp Sobolev inequality involving a Lorentz norm, and in the equivalent classical Hardy inequality. Limiting cases of the relevant inequalities are also considered.

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Published in:	Indiana University mathematics journal 2009-01, Vol.58 (3), p.1051-1096
Main Authors:	Cianchi, Andrea, Ferone, Adele
Format:	Article
Language:	English
Subjects:	Decreasing functions Embeddings Exact sciences and technology Fubinis theorem Function spaces General mathematics General, history and biography Integrable functions Mathematical constants Mathematical inequalities Mathematical theorems Mathematics Remainders Sciences and techniques of general use Sobolev spaces
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description	We exhibit the optimal norm for a remainder term in the sharp Sobolev inequality involving a Lorentz norm, and in the equivalent classical Hardy inequality. Limiting cases of the relevant inequalities are also considered.
doi_str_mv	10.1512/iumj.2009.58.3561
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subjects	Decreasing functions Embeddings Exact sciences and technology Fubinis theorem Function spaces General mathematics General, history and biography Integrable functions Mathematical constants Mathematical inequalities Mathematical theorems Mathematics Remainders Sciences and techniques of general use Sobolev spaces
title	Best Remainder Norms in Sobolev-Hardy Inequalities
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