This is a preview of subscription content, log in via an institution to check access.
References
Calderon A.P.: Inequalities for the maximal function relative to a metric. Stud. Math.57 (1976), 297–306
Capogna L., Danielli D., Garofalo N.: An embedding theorem and the Harnack inequality for nonlinear subelliptic equations. Commun. Partial Differ. Equations18 (1993), 1765–1794
Chanillo, S., Wheeden R.L.: Weighted Poincaré and Sobolev inequalities and estimates for the Peano maximal function. Am. J. Math.107 (1985), 1191–1226
Citti G., Garofalo N., Lanconelli E.: Harnack's inequality for sums of squares plus a potential. Am. J. Math.115 (1993), 699–734
Couhlon T.: Sobolev inequalities on graphs and on manifolds. Harmonic Analysis and Discrete Potential Theory. Picardello ed., Plenum Press, 1992
Couhlon T.: Inégalité de Gagliardo-Nirenberg pour les semi-groupes d'opérateurs et applications. Potential theory. (to appear)
Couhlon T., Saloff-Coste L.: Isopérimétrie pour les groupes et les variétés. Rev. Math. Iberoam.9 (1993), 293–314
Danielli D.: Representation formulas and embedding theorem for subelliptic operators. C.R. Acad. Sci., Paris Sér. I, Math.314 (1992), 987–990
David G., Semmes S.: StrongA ∞ weights, Sobolev inequalities and quasi-conformal mappings. Analysis and Partial Differential equations. Lect. Notes Pure Appl. Math.122 (1990), 101–111, Marcel Dekker, New York
Franchi B.: Weighted Sobolev-Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations. Trans. Am. Math. Soc.327 (1991), 125–158
Franchi B.: Inégalités de Sobolev pour des champs de vecteurs lipschitziens. C.R. Acad. Sci. Paris Sér. I, Math.311 (1990), 329–332
Franchi B.: Disuguaglianze di Sobolev e disuguaglianze isoperimétriche per metriche degeneri. In: Seminario di Analisi Matematica dell'Università di Bologna (January 1993), Bologna, 1993
Federer H.: Geometric Measure Theory Springer, 1969
Franchi B., Gallot S., Wheeden R.L.: Inégalités isopérimétriques pour des métriques dégénérées. C.R. Acad. Sci. Paris Sér. I, Math.317 (1993), 651–654
Franchi B., Gutierrez C., Wheeden R.L.: Weighted Sobolev-Poincaré inequalities for Grushin type operators. Commun. Partial Differ. Equations.19 (1994), 523–604
Franchi B., Lanconelli E.: Hölder regularity for a class of linear non uniformly elliptic operators with measurable coefficients. Ann. Sc. Norm. Super. Pisa (IV)10 (1983), 523–541
Fefferman C., Phong D.H.: Subelliptic eigenvalue problems. In: Conference on Harmonic Analysis, Chicago 1980, W. Beckner et al. ed. Wadsworth (1981), 590–606
Genebashvili I., Gogatishvili A., Kokilashvili V.: Criteria of general weak type inequalities for integral transforms with positive kernels. Proc. Georgian Acad. Sci. Math.1 (1993), 11–34
Jerison D., Sanchez-Calle A.: Subelliptic second order differential operators. Complex Analysis III. Lect. Notes Math.1277 (1987), Springer, 46–77
Long R.L., Nie F.S.: Weighted Sobolev inequality and eigenvalue estimates of Schrödinger operators. Harmonic Analysis (Tianjin, 1988). Lect. Notes Math. 1494, Springer, 1991
Lu G.: Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications. Rev. Mat. Iberoam.8 (1992), 367–439
Nagel A., Stein E.M., Wainger S.: Balls and metrics defined by vector fields I: basic properties. Acta Math.155 (1985), 103–147
Pansu P.: Une inégalité isopérimétrique sur le groupe de Heisenberg. C.R. Acad. Sci. Paris Sér. I, Math.295 (1985), 127–130
Saloff Coste L.: Inégalités de Sobolev produit sur les groupes de Lie nilpotents. J. Funct. Anal., 44–56
Saloff Coste L.: A note on Poincaré, Sobolev and Harnack inequalities. Int. Math. Res. Notices2 (1992), 27–38
Varopoulos N.Th.: Analysis on Lie groups. J. Funct. Anal.76 (1988), 364–410
Varopoulos N.Th.: Sobolev inequalities on Lie groups and symmetric spaces. J. Funct. Anal.86 (1989), 19–40
Varopoulos N.Th., Saloff Coste L., Couhlon T.: Analysis and geometry on groups. Camb. Tracts Math.100, 1993
Author information
Authors and Affiliations
Additional information
The first author was partially supported by MURST, Italy (40% and 60%) and GNAFA of CNR, Italy
The second author was partially supported by the European program GADGET
The third author was partially supported by NSF Grant # DMS91-04195
The first and third authors were also partially supported by a bilateral CNR-NSF project
Rights and permissions
About this article
Cite this article
Franchi, B., Gallot, S. & Wheeden, R.L. Sobolev and isoperimetric inequalities for degenerate metrics. Math. Ann. 300, 557–571 (1994). https://doi.org/10.1007/BF01450501
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01450501