p-Poincaré inequality versus ∞-Poincaré inequality: some counterexamples
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Ahlfors L., Beurling A.: The boundary correspondence under quasiconformal mappings. Acta Math. 96, 125–142 (1956)
Björn J., Shanmugalingam N.: Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces. J. Math. Anal. Appl. 332, 190–208 (2007)
Bourdon, M., Pajot, H.: Quasi-conformal geometry and hyperbolic geometry. (English summary) Rigidity in dynamics and geometry (Cambridge, 2000), pp. 1–17. Springer, Berlin (2002)
Björn J., Buckley S., Keith S.: Admissible measures in one dimension. Proc. Am. Math. Soc. 134(3), 703–705 (2006) (electronic)
Björn, A., Björn, J.: Nonlinear potential theory on metric spaces, EMS Tracts Mathematics, European Math. Soc., Zurich (to appear)
Burago, D., Burago, Y., Ivanov, S.: A Course in Metric Geometry. Graduate Studies in Mathematics. vol. 33. American Mathematical Society, Providence (2001)
Cheeger J.: Differentiability of Lipschitz functions on metric measure spaces. Geom. Funct. Anal. 9, 428–517 (1999)
Durand-Cartagena E., Jaramillo J.A.: Pointwise Lipschitz functions on metric spaces. J. Math. Anal. Appl. 363, 525–548 (2010)
Durand-Cartagena, E., Jaramillo, J.A., Shanmugalingam, N.: The ∞-Poincaré inequality in metric measure spaces. Mich. Math. J. 60 (2011, to appear)
Falconer K.: Fractal Geometry: Mathematical Foundations and Applications, 2nd edn. Wiley, New York (2003)
Folland, G.B.: Real Analysis, Modern Techniques and Their Applications. Pure and Applied Mathematics. Wiley, New York (1999)
Fukaya K.: Collapsing of Riemannian manifolds and eigenvalues of Laplace operator. Invent. Math. 87(3), 517–547 (1987)
Gromov, M.: Structures métriques pour les variétiés riemanniennes. In: Lafontaine, J., Pansu, P. (ed.) Textes Mathématiques 1. Cedic/Nathan, Paris (1981)
Hajłasz P., Koskela P.: Sobolev met Poincaré. Sobolev met Poincaré. Mem. Am. Math. Soc. 145(688), x+101 (2000)
Heinonen J., Koskela P.: Quasiconformal maps in metric spaces with controlled geometry. Acta Math. 181, 1–61 (1998)
Heinonen, J., Kilpeläinen, T., Martio, O.: Nonlinear Potential Theory of Degenerate Elliptic Equations. Unabridged republication of the 1993 original, pp. xii+404. Dover Publications Inc., Mineola (2006)
Keith, S.: A differentiable structure for metric measure spaces, Dissertation. University of Michigan (2002)
Keith S.: Modulus and the Poincaré inequality on metric measure spaces. Math. Z. 245, 255–292 (2003)
Koskela P., McManus P.: Quasiconformal mappings and Sobolev spaces. Studia Math. 131(1), 1–17 (1998)
Keith S., Zhong X.: The Poincaré inequality is an open ended condition. Ann. Math. 167(2), 575–599 (2008)
Mattila P.: Geometry of Sets and Measures in Euclidean Spaces: Fractals and rectifiability, Cambridge studies in Advance Mathematics, vol. 44. Cambridge University Press, New York (1995)
Semmes S.: Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities. Selecta Math., New Series 2(2), 155–295 (1996)
Semmes S.: Some Novel Types of Fractal Geometry. Oxford Science Publications, New York (2001)
Shanmugalingam N.: Newtonian spaces: an extension of Sobolev spaces to metric measure spaces. Rev. Mat. Iberoamericana 16, 243–279 (2000)
Shanmugalingam, N.: Newtonian spaces: an extension of Sobolev spaces to metric measure spaces, Ph.D. thesis, University of Michigan http://www.math.uc.edu/~nages/papers.html (1999)
Stein, E.M.: Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. With the assistance of Timothy S. Murphy. Princeton Mathematical Series, vol. 43. Monographs in Harmonic Analysis, III. Princeton University Press, Princeton (1993)
Väisälä, J.: Lectures on n-dimensional quasiconformal mappings. Lecture Notes in Mathematics, vol. 229, Springer, Berlin (1971)
Zygmund, A.: Trigonometric series. Vols. I, II, 2nd edn., vol. I, pp. xii+383; vol. II, pp. vii+354. Cambridge University Press, New York (1959)