Further study on domains and quasihyperbolic distances

We establish constructive geometric tools for determining when a domain is L s -averaging and obtain upper and lower bounds for the L s -integrals of the quasihyperbolic distance. We also construct examples that are helpful to understand our geometric tools and the relationship between p -Poincaré d...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2022; no. 1; pp. 1 - 23
Main Authors Ding, Shusen, Helliwell, Dylan, Pandya, Gavin, Yae, Arya
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 11.11.2022
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Domains
L s $L^{s}$ -averaging domain
Lower bounds
Mathematics
Mathematics and Statistics
Partial differential equations
Poincaré domain
Quasihyperbolic distance
Whitney subdivision
Poincaré domain
averaging domain
Quasihyperbolic distance
Whitney subdivision
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Summary:We establish constructive geometric tools for determining when a domain is L s -averaging and obtain upper and lower bounds for the L s -integrals of the quasihyperbolic distance. We also construct examples that are helpful to understand our geometric tools and the relationship between p -Poincaré domains and L s -averaging domains. Finally, finite unions of L s ( μ ) -averaging domains are explored.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-022-02882-1