Compensation couples and isoperimetric estimates for vector fields

Bruno Franchi; Richard Wheeden

Colloquium Mathematicae (1997)

  • Volume: 74, Issue: 1, page 9-27
  • ISSN: 0010-1354

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Franchi, Bruno, and Wheeden, Richard. "Compensation couples and isoperimetric estimates for vector fields." Colloquium Mathematicae 74.1 (1997): 9-27. <http://eudml.org/doc/210506>.

@article{Franchi1997,
author = {Franchi, Bruno, Wheeden, Richard},
journal = {Colloquium Mathematicae},
keywords = {isoperimetric inequality; smooth vector fields; Hörmander’s condition of order ; subunit curve; compensation couple; characteristic points},
language = {eng},
number = {1},
pages = {9-27},
title = {Compensation couples and isoperimetric estimates for vector fields},
url = {http://eudml.org/doc/210506},
volume = {74},
year = {1997},
}

TY - JOUR
AU - Franchi, Bruno
AU - Wheeden, Richard
TI - Compensation couples and isoperimetric estimates for vector fields
JO - Colloquium Mathematicae
PY - 1997
VL - 74
IS - 1
SP - 9
EP - 27
LA - eng
KW - isoperimetric inequality; smooth vector fields; Hörmander’s condition of order ; subunit curve; compensation couple; characteristic points
UR - http://eudml.org/doc/210506
ER -

References

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  2. [CDG] L. Capogna, D. Danielli and N. Garofalo, The geometric Sobolev embedding for vector fields and the isoperimetric inequality, Comm. Anal. Geom. 2 (1994), 203-215. Zbl0864.46018
  3. [CW] R. R. Coifman et G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, 1971, 1-158. 
  4. [CUN] D. Cruz-Uribe, SFO, and C. J. Neugebauer, The structure of the reverse Hölder classes, Trans. Amer. Math. Soc. 347 (1995), 2941-2960. Zbl0851.42016
  5. [FP] C. Fefferman and D. H. Phong, Subelliptic eigenvalue estimates, in: Conference on Harmonic Analysis in Honor of A. Zygmund, Chicago, 1980, W. Beckner et al. (eds.), Wadsworth, 1981, 590-606. 
  6. [F] B. Franchi, Weighted Sobolev-Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations, Trans. Amer. Math. Soc. 327 (1991), 125-158. Zbl0751.46023
  7. [FGaW1] B. Franchi, S. Gallot et R. L. Wheeden, Inégalités isopérimétriques pour des métriques dégénérées, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 651-654. 
  8. [FGaW2] B. Franchi, S. Gallot et R. L. Wheeden, Sobolev and isoperimetric inequalities for degenerate metrics, Math. Ann. 300 (1994), 557-571. Zbl0830.46027
  9. [FGuW] B. Franchi, C. E. Gutiérrez and R. L. Wheeden, Weighted Sobolev-Poincaré inequalities for Grushin type operators, Comm. Partial Differential Equations 19 (1994), 523-604. Zbl0822.46032
  10. [FLW] B. Franchi, G. Lu and R. L. Wheeden, Representation formulas and weighted Poincaré inequalities for Hörmander vector fields, Ann. Inst. Fourier (Grenoble) 45 (1995), 577-604. Zbl0820.46026
  11. [G] M. Gromov, Carnot-Carathéodory spaces seen from within, Prépublications de l'IHES (1994). Zbl0864.53025
  12. [H] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Grundlehren Math. Wiss. 256, Springer, Berlin, 1983. 
  13. [NSW] A. Nagel, E. M. Stein and S. Wainger, Balls and metrics defined by vector fields I: basic properties, Acta Math. 155 (1985), 103-147. Zbl0578.32044
  14. [S] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, 1993. Zbl0821.42001

Citations in EuDML Documents

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  1. Piotr Hajłasz, Jacob Mirra, The Lusin Theorem and Horizontal Graphs in the Heisenberg Group
  2. Bruno Franchi, Piotr Hajłasz, How to get rid of one of the weights in a two-weight Poincaré inequality?
  3. Francesco Borrello, Degenerate Elliptic Equations and Morrey Spaces
  4. Franchi, Bruno, spaces and rectifiability for Carnot-Carathéodory metrics: an introduction

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