Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 693-697

NOTES ON ADMISSIBLE MEASURES IN ONE DIMENSION

Shiliang Zhao

Fudan University, Department of Mathematics
220 Handan Road, Shanghai 200433; P.R. China; zhaoshiliang2013 'at' gmail.com

Abstract. μ is called a p-admissible measure in one dimension if it is a doubling measure that supports a (1,p)-Poincaré inequality. In this note, we estimate the range of p that (1,p)-Poincaré inequality holds on (R,|·|,μ) where |·| is the Euclidean metric.

2010 Mathematics Subject Classification: Primary 26D10; Secondary 46E35.

Key words: p-admissible measures, Poincaré inequality.

Reference to this article: S. Zhao: Notes on admissible measures in one dimension. Ann. Acad. Sci. Fenn. Math. 41 (2016), 693-697.

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doi:10.5186/aasfm.2016.4140