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(2000)
Between Sobolev and Poincaré. Geometric aspects of functional analysis
- Publisher
- Springer International Publishing
- Copyright
- © Springer Nature Switzerland AG 2019
- ISBN
- 978-3-030-26390-4
- Pages
- 55 –69
- DOI
- 10.1007/978-3-030-26391-1_6
- Publisher site
- See Chapter on Publisher Site
Abstract
[We show sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order d − 1 for any d∈ℕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$d \in \mathbb {N}$$ \end{document}. Here we focus on differentiable functions on the Euclidean space in presence of a Poincaré-type inequality. The bounds are based on d-th order derivatives.]
Published: Nov 27, 2019
Keywords: Concentration of measure phenomenon; Poincaré inequalities; Primary 60E15; 60F10; Secondary 60B20