Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nash type inequalities for fractional powers of non-negative self-adjoint operators


Authors: Alexander Bendikov and Patrick Maheux
Journal: Trans. Amer. Math. Soc. 359 (2007), 3085-3097
MSC (2000): Primary 39B62, 47A60, 26A12, 26A33, 81Q10
Published electronically: January 25, 2007
MathSciNet review: 2299447
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator $ A$, we prove a Nash type inequality for the fractional powers $ A^{\alpha}$ of $ A$. Under some assumptions, we give ultracontractivity bounds for the semigroup $ (T_{t,{\alpha}})$ generated by $ -A^{\alpha}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 39B62, 47A60, 26A12, 26A33, 81Q10

Retrieve articles in all journals with MSC (2000): 39B62, 47A60, 26A12, 26A33, 81Q10


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: http://dx.doi.org/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
Published electronically: 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)
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.