Harmonic functions with BMO traces and their limiting behaviors on metric measure spaces

Jin, Yutong; Li, Bo; Shen, Tianjun

doi:10.1007/s40840-023-01603-1

Bull. Malays. Math. Sci. Soc.

2023

DOI: 10.1007/s40840-023-01603-1

|View full text |Cite

Harmonic functions with BMO traces and their limiting behaviors on metric measure spaces

Yutong Jin,

Bo Li,

Tianjun Shen

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Solutions of Weinstein type equations, Carleson measures and BMO(R+,dmλ
Guo,
Betancor,
Yang
2024
Journal of Mathematical Analysis and Applications
0
0
0
0
View full text Add to dashboard Cite

On the Coincidence between Campanato Functions and Lipschitz Functions: A New Approach via Elliptic PDES

Li,

Lin

et al. 2024

The Quarterly Journal of Mathematics

View full text Add to dashboard Cite

Let $({\mathcal{M}},d,\mu)$ be the metric measure space with a Dirichlet form $\mathscr{E}$. In this paper, we obtain that the Campanato function and the Lipschitz function do always coincide. Our approach is based on the harmonic extension technology, which extends a function u on ${\mathcal{M}}$ to its Poisson integral Ptu on ${\mathcal{M}}\times\mathbb{R}_+$. With this tool in hand, we can utilize the same Carleson measure condition of the Poisson integral to characterize its Campanato/Lipschitz trace, and hence, they are equivalent to each other. This equivalence was previously obtained by Macías–Segovia [Adv. Math., 1979]. However, we provide a new proof, via the boundary value problem for the elliptic equation. This result indicates the famous saying of Stein–Weiss at the beginning of Chapter II in their book [Princeton Mathematical Series, No. 32, 1971].

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Harmonic functions with BMO traces and their limiting behaviors on metric measure spaces

Cited by 2 publications

References 50 publications

Solutions of Weinstein type equations, Carleson measures and BMO(R+,dmλ
Guo,
Betancor,
Yang
2024
Journal of Mathematical Analysis and Applications
0
0
0
0
View full text Add to dashboard Cite

Solutions of Weinstein type equations, Carleson measures and BMO(R+,dmλ
Guo,
Betancor,
Yang
2024
Journal of Mathematical Analysis and Applications
0
0
0
0
View full text Add to dashboard Cite

On the Coincidence between Campanato Functions and Lipschitz Functions: A New Approach via Elliptic PDES

Contact Info

Product

Resources

About

Harmonic functions with BMO traces and their limiting behaviors on metric measure spaces

Cited by 2 publications

References 50 publications

Solutions of Weinstein type equations, Carleson measures and BMO(R+,dmλGuo, Betancor, Yang 2024Journal of Mathematical Analysis and Applications0000View full textAdd to dashboardCite

Solutions of Weinstein type equations, Carleson measures and BMO(R+,dmλGuo, Betancor, Yang 2024Journal of Mathematical Analysis and Applications0000View full textAdd to dashboardCite

On the Coincidence between Campanato Functions and Lipschitz Functions: A New Approach via Elliptic PDES

Contact Info

Product

Resources

About

Solutions of Weinstein type equations, Carleson measures and BMO(R+,dmλ
Guo,
Betancor,
Yang
2024
Journal of Mathematical Analysis and Applications
0
0
0
0
View full text Add to dashboard Cite

Solutions of Weinstein type equations, Carleson measures and BMO(R+,dmλ
Guo,
Betancor,
Yang
2024
Journal of Mathematical Analysis and Applications
0
0
0
0
View full text Add to dashboard Cite