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.

Saved in:
Bibliographic Details
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
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2009.58.3561