Maximal Function Estimates and Self-improvement Results for Poincaré Inequalities

Juha Kinnunen; Juha Lehrbäck; Antti V. Vähäkangas; Xiao Zhong

Maximal Function Estimates and Self-improvement Results for Poincaré Inequalities

Juha Kinnunen, Juha Lehrbäck, Antti V. Vähäkangas, Xiao Zhong

University of Jyväskylä

Research output: Contribution to journal › Article › Scientific

Abstract

Our main result is an estimate for a sharp maximal function, which implies a Keith–
Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.

Original language	English
Number of pages	21
Journal	arXiv.org
Publication status	Published - 2017
MoE publication type	Not Eligible

Keywords

Analysis on metric spaces
Sobolev spaces
Poincaré inequality
geodesic space

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https://arxiv.org/pdf/1705.05072.pdf

Cite this

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title = "Maximal Function Estimates and Self-improvement Results for Poincar{\'e} Inequalities",

abstract = "Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincar{\'e} inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.",

keywords = "Analysis on metric spaces, Sobolev spaces, Poincar{\'e} inequality, geodesic space",

author = "Juha Kinnunen and Juha Lehrb{\"a}ck and V{\"a}h{\"a}kangas, {Antti V.} and Xiao Zhong",

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journal = "arXiv.org",

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T1 - Maximal Function Estimates and Self-improvement Results for Poincaré Inequalities

AU - Kinnunen, Juha

AU - Lehrbäck, Juha

AU - Vähäkangas, Antti V.

AU - Zhong, Xiao

PY - 2017

Y1 - 2017

N2 - Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.

AB - Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.

KW - Analysis on metric spaces

KW - Sobolev spaces

KW - Poincaré inequality

KW - geodesic space

M3 - Article

JO - arXiv.org

JF - arXiv.org

ER -

Maximal Function Estimates and Self-improvement Results for Poincaré Inequalities

Abstract

Keywords

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