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Nash type inequalities for fractional powers of non-negative self-adjoint operators
Author(s):
Alexander
Bendikov;
Patrick
Maheux
Journal:
Trans. Amer. Math. Soc.
359
(2007),
3085-3097.
MSC (2000):
Primary 39B62, 47A60, 26A12, 26A33, 81Q10
Posted:
January 25, 2007
MathSciNet review:
2299447
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Additional information
Abstract:
Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator  , we prove a Nash type inequality for the fractional powers  of  . Under some assumptions, we give ultracontractivity bounds for the semigroup  generated by  .
References:
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Additional Information:
Alexander
Bendikov
Affiliation:
Mathematical Institute of the Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Email:
bendikov@math.uni.wroc.pl
Patrick
Maheux
Affiliation:
Département de Mathématiques, MAPMO-Fédération Denis Poisson, Université d'Or- léans, BP 6759, F 45 067 Orleans Cedex 2, France
Email:
pmaheux@univ-orleans.fr
DOI:
10.1090/S0002-9947-07-04020-2
PII:
S 0002-9947(07)04020-2
Keywords:
Nash inequality,
fractional powers of operators,
semigroup of operators,
logarithmic Sobolev inequality,
ultracontractivity property,
Dirichlet form
Received by editor(s):
March 11, 2002
Received by editor(s) in revised form:
April 11, 2005
Posted:
January 25, 2007
Additional Notes:
This research was partially supported by the European Commission (IHP Network ``Harmonic Analysis and Related Problems'' 2002-2006, contract HPRN-CT-2001-00273-HARP)
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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