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Optimal Sobolev imbeddings
-
Ron Kerman
and
Luboš Pick
Published/Copyright:
August 14, 2006
Abstract
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.
Received: 2004-01-26
Revised: 2004-06-25
Published Online: 2006-08-14
Published in Print: 2006-07-01
© Walter de Gruyter
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Articles in the same Issue
- Optimal Sobolev imbeddings
- On spectral gaps and exit time distributions for a non-smooth domain
- Sums of three squares over imaginary quadratic fields
- Totally projective unit groups in modular abelian group algebras
- Wellposedness and asymptotic behaviour of non-autonomous boundary Cauchy problems
- On large deviations for random currents induced from stochastic line integrals
- A bound for the 3-part of class numbers of quadratic fields by means of the square sieve
- On a question of Lillian Pierce
