Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jfa.2008.05.012
Title: Self-improving properties of inequalities of Poincaré type on measure spaces and applications
Authors: Chua, S.-K. 
Wheeden, R.L.
Keywords: Global Poincaré estimates
Power type weights
Quasimetric spaces
s-John domains
Issue Date: 1-Dec-2008
Citation: Chua, S.-K., Wheeden, R.L. (2008-12-01). Self-improving properties of inequalities of Poincaré type on measure spaces and applications. Journal of Functional Analysis 255 (11) : 2977-3007. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jfa.2008.05.012
Abstract: We show that the self-improving nature of Poincaré estimates persists for domains in rather general measure spaces. We consider both weak type and strong type inequalities, extending techniques of B. Franchi, C. Pérez and R. Wheeden. As an application in spaces of homogeneous type, we derive global Poincaré estimates for a class of domains with rough boundaries that we call φ{symbol}-John domains, and we show that such domains have the requisite properties. This class includes John (or Boman) domains as well as s-John domains. Further applications appear in a companion paper. © 2008 Elsevier Inc. All rights reserved.
Source Title: Journal of Functional Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/104086
ISSN: 00221236
DOI: 10.1016/j.jfa.2008.05.012
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