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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 $-A^{\alpha }$.
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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