Poincaré inequalities with exact missing terms on homogeneous groups

Tohru Ozawa; Durvudkhan Suragan

doi:10.2969/JMSJ/83738373

Poincaré inequalities with exact missing terms on homogeneous groups

Tohru Ozawa
, Durvudkhan Suragan

Waseda University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we present exact missing terms for the Poincaré 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 Poincaré inequality for the Dirichlet Laplacian.

Original language	English
Pages (from-to)	497-503
Number of pages	7
Journal	Journal of the Mathematical Society of Japan
Volume	73
Issue number	2
DOIs	https://doi.org/10.2969/JMSJ/83738373
Publication status	Published - Apr 2021

Funding

2010 Mathematics Subject Classification. Primary 39B62; Secondary 39B99, 22E30. Key Words and Phrases. Poincaré 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.

Keywords

Homogeneous group
Optimal constant
Poincaré inequality
Sharp remainder

ASJC Scopus subject areas

General Mathematics

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10.2969/JMSJ/83738373

Cite this

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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",

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T1 - Poincaré inequalities with exact missing terms on homogeneous groups

AU - Ozawa, Tohru

AU - Suragan, Durvudkhan

N1 - Funding Information: 2010 Mathematics Subject Classification. Primary 39B62; Secondary 39B99, 22E30. Key Words and Phrases. Poincaré 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: © 2021 The Mathematical Society of Japan

PY - 2021/4

Y1 - 2021/4

N2 - In this paper, we present exact missing terms for the Poincaré 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 Poincaré inequality for the Dirichlet Laplacian.

AB - In this paper, we present exact missing terms for the Poincaré 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 Poincaré inequality for the Dirichlet Laplacian.

KW - Homogeneous group

KW - Optimal constant

KW - Poincaré inequality

KW - Sharp remainder

UR - https://www.scopus.com/pages/publications/85105933811

UR - https://www.scopus.com/pages/publications/85105933811#tab=citedBy

U2 - 10.2969/JMSJ/83738373

DO - 10.2969/JMSJ/83738373

M3 - Article

AN - SCOPUS:85105933811

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VL - 73

SP - 497

EP - 503

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 2

ER -

Poincaré inequalities with exact missing terms on homogeneous groups

Abstract

Funding

Keywords

ASJC Scopus subject areas

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