@article{b707529b465648ad894d0f73f87453f0,
title = "Poincar{\'e} inequalities with exact missing terms on homogeneous groups",
abstract = "In this paper, we present exact missing terms for the Poincar{\'e} inequalities on homogeneous groups. We also discuss some consequences in the Euclidean cases. Thus, we have succeeded in finding a simple proof of the sharp Poincar{\'e} inequality for the Dirichlet Laplacian.",
keywords = "Homogeneous group, Optimal constant, Poincar{\'e} inequality, Sharp remainder",
author = "Tohru Ozawa and Durvudkhan Suragan",
note = "Funding Information: 2010 Mathematics Subject Classification. Primary 39B62; Secondary 39B99, 22E30. Key Words and Phrases. Poincar{\'e} inequality, sharp remainder, optimal constant, homogeneous group. The authors were supported in parts by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University grant 240919FD3901. No new data was collected or generated during the course of this research. Publisher Copyright: {\textcopyright} 2021 The Mathematical Society of Japan",
year = "2021",
month = apr,
doi = "10.2969/JMSJ/83738373",
language = "English",
volume = "73",
pages = "497--503",
journal = "Journal of the Mathematical Society of Japan",
issn = "0025-5645",
publisher = "Mathematical Society of Japan - Kobe University",
number = "2",
}