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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Hardy inequalities with optimal constants and remainder terms
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by Filippo Gazzola, Hans-Christoph Grunau and Enzo Mitidieri PDF
Trans. Amer. Math. Soc. 356 (2004), 2149-2168 Request permission

Abstract:

We show that the classical Hardy inequalities with optimal constants in the Sobolev spaces $W_0^{1,p}$ and in higher-order Sobolev spaces on a bounded domain $\Omega \subset \mathbb {R}^n$ can be refined by adding remainder terms which involve $L^p$ norms. In the higher-order case further $L^p$ norms with lower-order singular weights arise. The case $1<p<2$ being more involved requires a different technique and is developed only in the space $W_0^{1,p}$.
References
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Additional Information
  • Filippo Gazzola
  • Affiliation: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy
  • Email: gazzola@mate.polimi.it
  • Hans-Christoph Grunau
  • Affiliation: Fakultät für Mathematik, Otto-von-Guericke-Universität, Postfach 4120, D-39016 Magdeburg, Germany
  • Email: Hans-Christoph.Grunau@mathematik.uni-magdeburg.de
  • Enzo Mitidieri
  • Affiliation: Dipartimento di Scienze Matematiche, Via A. Valerio 12/1, Università degli Studi di Trieste, I-34100 Trieste, Italy
  • Email: mitidier@univ.trieste.it
  • Received by editor(s): June 20, 2000
  • Received by editor(s) in revised form: May 8, 2003
  • Published electronically: December 9, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 2149-2168
  • MSC (2000): Primary 46E35; Secondary 35B50, 35J40
  • DOI: https://doi.org/10.1090/S0002-9947-03-03395-6
  • MathSciNet review: 2048513