A maximal Function Approach to Two-Measure Poincaré Inequalities
Abstract
This paper extends the self-improvement result of Keith and Zhong in Keith and Zhong (Ann. Math. 167(2):575–599, 2008) to the two-measure case. Our main result shows that a two-measure (p, p)-Poincaré inequality for 10 under a balance condition on the measures. The corresponding result for a maximal Poincaré inequality is also considered. In this case the left-hand side in the Poincaré inequality is replaced with an integral of a sharp maximal function and the results hold without a balance condition. Moreover, validity of maximal Poincaré inequalities is used to characterize the self-improvement of two-measure Poincaré inequalities. Examples are constructed to illustrate the role of the assumptions. Harmonic analysis and PDE techniques are used extensively in the arguments.
Main Authors
Format
Articles
Research article
Published
2019
Series
Subjects
Publication in research information system
Publisher
Springer New York
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201906253435Use this for linking
Review status
Peer reviewed
ISSN
1050-6926
DOI
https://doi.org/10.1007/s12220-018-0061-z
Language
English
Published in
Journal of Geometric Analysis
Citation
- Kinnunen, J., Korte, R., Lehrbäck, J., & Vähäkangas, A. (2019). A maximal Function Approach to Two-Measure Poincaré Inequalities. Journal of Geometric Analysis, 29(2), 1763-1810. https://doi.org/10.1007/s12220-018-0061-z
License
Copyright© Mathematica Josephina, Inc. 2018