Please use this identifier to cite or link to this item: https://doi.org/10.1017/S0024611506015826
Title: Estimates of best constants for weighted poincaré inequalities on convex domains
Authors: Chua, S.-K. 
Wheeden, R.L.
Issue Date: Jul-2006
Citation: Chua, S.-K., Wheeden, R.L. (2006-07). Estimates of best constants for weighted poincaré inequalities on convex domains. Proceedings of the London Mathematical Society 93 (1) : 197-226. ScholarBank@NUS Repository. https://doi.org/10.1017/S0024611506015826
Abstract: Let 1 ≤ q ≤ p < ∞ and let C be the class of all bounded convex domains Ω in ℝn, Following the approach in [1], we show that the best constant C in the weighted Poincaré inequality equation presented for all Ω ∈ C, all Lipschitz continuous functions f on Ω, and all weights w which are any positive power of a non-negative concave function on Ω is the same as the best constant for the corresponding one-dimensional situation, where C reduces to the class of bounded intervals. Using facts from [9], we estimate the best constant. In the case q = 1 and 1 < p < ∞, our estimate is between the best constant and twice the best constant. Furthermore, when p = q = 1 or p = q = 2, the estimate is sharp. Finally, in the case where the domains in Rn are further restricted to be parallelepipeds, we obtain a slightly different form of Poincaré's inequality which is better adapted to directional derivatives and the sidelengths of the parallelepipeds. We also show that this estimate is sharp for a fixed rectangle. © 2006 London Mathematical Society.
Source Title: Proceedings of the London Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/103212
ISSN: 00246115
DOI: 10.1017/S0024611506015826
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

17
checked on Aug 15, 2018

WEB OF SCIENCETM
Citations

16
checked on Aug 15, 2018

Page view(s)

31
checked on Aug 3, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.