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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On uniform properties of doubling measures
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by Michael Ruzhansky PDF
Proc. Amer. Math. Soc. 129 (2001), 3413-3416 Request permission


In this paper we prove that if $(X,d,\mu )$ is a metric doubling space with segment property, then $\inf r(E)/r(B)>0$ if and only if $\inf \mu (E)/\mu (B)>0$, where the infimum is taken over any collection $\mathcal {C}$ of balls $E, B$ such that $E\subset B\subset X$. As a consequence we show that if $X$ is a linear metric doubling space, then it must be finite dimensional.
  • Bruno Franchi, Guozhen Lu, and Richard L. Wheeden, A relationship between Poincaré-type inequalities and representation formulas in spaces of homogeneous type, Internat. Math. Res. Notices 1 (1996), 1–14. MR 1383947, DOI 10.1155/S1073792896000013
  • Y. Liu, G. Lu and R.L. Wheeden, ‘Some equivalent definitions of high order Sobolev spaces on stratified groups and generalizations to metric spaces’, preprint.
  • Yongping Liu, Guozhen Lu, and Richard L. Wheeden, Representation formulas and Sobolev spaces of high order on stratified groups and generalizations to metric spaces, Math. Sci. Res. Hot-Line 3 (1999), no. 7, 35–59. MR 1702600
  • Guozhen Lu, Local and global interpolation inequalities on the Folland-Stein Sobolev spaces and polynomials on stratified groups, Math. Res. Lett. 4 (1997), no. 6, 777–790. MR 1492120, DOI 10.4310/MRL.1997.v4.n6.a1
  • G. Lu, S. Pedersen and M. Ruzhansky, ‘Distribution theory, high order gradients and polynomials on metric spaces’, in preparation.
  • Guozhen Lu and Richard L. Wheeden, Poincaré inequalities, isoperimetric estimates, and representation formulas on product spaces, Indiana Univ. Math. J. 47 (1998), no. 1, 123–151. MR 1631545, DOI 10.1512/iumj.1998.47.1494
  • G. Lu and R.L. Wheeden, ‘High order representation formulas and embedding theorems on stratified groups and generalizations’, to appear in Studia Math.
  • Nobuaki Obata, White noise calculus and Fock space, Lecture Notes in Mathematics, vol. 1577, Springer-Verlag, Berlin, 1994. MR 1301775, DOI 10.1007/BFb0073952
  • François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
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Additional Information
  • Michael Ruzhansky
  • Affiliation: Department of Mathematics and Statistics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
  • Address at time of publication: Department of Mathematics, Imperial College, 180 Queen’s Gate, London SW7 2BZ, England
  • MR Author ID: 611131
  • Email:,
  • Received by editor(s): November 23, 1999
  • Received by editor(s) in revised form: March 24, 2000
  • Published electronically: May 3, 2001
  • Communicated by: Christopher D. Sogge
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3413-3416
  • MSC (2000): Primary 54E35, 54E50, 46A03, 28E15
  • DOI:
  • MathSciNet review: 1845020