Admissible measures in one dimension
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- by Jana Björn, Stephen Buckley and Stephen Keith PDF
- Proc. Amer. Math. Soc. 134 (2006), 703-705 Request permission
Abstract:
In this note we show that $p\mspace {1mu}$-admissible measures in one dimension (i.e. doubling measures admitting a $p\mspace {1mu}$-Poincaré inequality) are precisely the Muckenhoupt $A_p$-weights.References
- Seng-Kee Chua and Richard L. Wheeden, Sharp conditions for weighted 1-dimensional Poincaré inequalities, Indiana Univ. Math. J. 49 (2000), no. 1, 143–175. MR 1777034, DOI 10.1512/iumj.2000.49.1754
- Eugene B. Fabes, Carlos E. Kenig, and Raul P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), no. 1, 77–116. MR 643158, DOI 10.1080/03605308208820218
- Piotr Hajłasz and Pekka Koskela, Sobolev meets Poincaré, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 10, 1211–1215 (English, with English and French summaries). MR 1336257
- Juha Heinonen, Tero Kilpeläinen, and Olli Martio, Nonlinear potential theory of degenerate elliptic equations, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1993. Oxford Science Publications. MR 1207810
- Juha Heinonen and Pekka Koskela, Weighted Sobolev and Poincaré inequalities and quasiregular mappings of polynomial type, Math. Scand. 77 (1995), no. 2, 251–271. MR 1379269, DOI 10.7146/math.scand.a-12564
- Keith, S. and Zhong, X., The Poincaré inequality is an open ended condition, Preprint, Jyväskylä 2003
- Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
Additional Information
- Jana Björn
- Affiliation: Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
- Email: jabjo@mai.liu.se
- Stephen Buckley
- Affiliation: Department of Mathematics, National University of Ireland, Maynooth, County Kildare, Ireland
- Email: sbuckley@maths.may.ie
- Stephen Keith
- Affiliation: Centre for Mathematics and its Application, Australian National University, Canberra, ACT 0200, Australia
- Email: keith@maths.anu.edu.au
- Received by editor(s): July 6, 2004
- Published electronically: September 28, 2005
- Additional Notes: The first author was supported by the Swedish Research Council and Gustaf Sigurd Magnuson’s fund of the Royal Swedish Academy of Sciences, and completed this research while at Lund University.
The second author was partially supported by Enterprise Ireland.
The third author was supported by the Australian Research Council. - Communicated by: Andreas Seeger
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 703-705
- MSC (2000): Primary 26D10; Secondary 46E35
- DOI: https://doi.org/10.1090/S0002-9939-05-07925-6
- MathSciNet review: 2180887