Nash type inequalities for fractional powers of non-negative self-adjoint operators
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- by Alexander Bendikov and Patrick Maheux PDF
- Trans. Amer. Math. Soc. 359 (2007), 3085-3097 Request permission
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
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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
- 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)
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 3085-3097
- MSC (2000): Primary 39B62, 47A60, 26A12, 26A33, 81Q10
- DOI: https://doi.org/10.1090/S0002-9947-07-04020-2
- MathSciNet review: 2299447