Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9939-06-08545-5
Title: A note on sharp 1-dimensional poincaré inequalities
Authors: Chua, S.-K. 
Wheeden, R.L.
Keywords: Hardy inequalities
Poincaré inequalities
Sobolev inequalities
Issue Date: Aug-2006
Citation: Chua, S.-K., Wheeden, R.L. (2006-08). A note on sharp 1-dimensional poincaré inequalities. Proceedings of the American Mathematical Society 134 (8) : 2309-2316. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9939-06-08545-5
Abstract: Let 1 < p < ∞ and -∞ < a < b < ∞. We show by using elementary methods that the best constant C (necessarily independent of a and b) for which the 1-dimensional Poincaré inequality ∥f - f av∥ L1[a,b] ≤ C(b - a) 2-1/p ∥f′∥ Lp[a,b] holds for all Lipschitz continuous functions f, with f av = f a b f / (b - a), is C = 1/2(1 + p′) -1/p′. © 2006 American Mathematical Society.
Source Title: Proceedings of the American Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/102710
ISSN: 00029939
DOI: 10.1090/S0002-9939-06-08545-5
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