Refined Hardy inequalities

Hajer Bahouri; Jean-Yves Chemin; Isabelle Gallagher

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

  • Volume: 5, Issue: 3, page 375-391
  • ISSN: 0391-173X

Abstract

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The aim of this article is to present “refined” Hardy-type inequalities. Those inequalities are generalisations of the usual Hardy inequalities, their additional feature being that they are invariant under oscillations: when applied to highly oscillatory functions, both sides of the refined inequality are of the same order of magnitude. The proof relies on paradifferential calculus and Besov spaces. It is also adapted to the case of the Heisenberg group.

How to cite

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Bahouri, Hajer, Chemin, Jean-Yves, and Gallagher, Isabelle. "Refined Hardy inequalities." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.3 (2006): 375-391. <http://eudml.org/doc/242839>.

@article{Bahouri2006,
abstract = {The aim of this article is to present “refined” Hardy-type inequalities. Those inequalities are generalisations of the usual Hardy inequalities, their additional feature being that they are invariant under oscillations: when applied to highly oscillatory functions, both sides of the refined inequality are of the same order of magnitude. The proof relies on paradifferential calculus and Besov spaces. It is also adapted to the case of the Heisenberg group.},
author = {Bahouri, Hajer, Chemin, Jean-Yves, Gallagher, Isabelle},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {375-391},
publisher = {Scuola Normale Superiore, Pisa},
title = {Refined Hardy inequalities},
url = {http://eudml.org/doc/242839},
volume = {5},
year = {2006},
}

TY - JOUR
AU - Bahouri, Hajer
AU - Chemin, Jean-Yves
AU - Gallagher, Isabelle
TI - Refined Hardy inequalities
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2006
PB - Scuola Normale Superiore, Pisa
VL - 5
IS - 3
SP - 375
EP - 391
AB - The aim of this article is to present “refined” Hardy-type inequalities. Those inequalities are generalisations of the usual Hardy inequalities, their additional feature being that they are invariant under oscillations: when applied to highly oscillatory functions, both sides of the refined inequality are of the same order of magnitude. The proof relies on paradifferential calculus and Besov spaces. It is also adapted to the case of the Heisenberg group.
LA - eng
UR - http://eudml.org/doc/242839
ER -

References

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