English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The existence and nonexistence of $\lambda$-harmonic functions in unboundeddomains of $\mathbb{H}^n$ are investigated. We prove that if the $(n-1)/2$Hausdorff measure of the asymptotic boundary of a domain $\Omega$ is zero, thenthere is no bounded $\lambda$-harmonic function of $\Omega$ for $\lambda \in[0,\lambda_1(\mathbb{H}^n)]$, where $\lambda_1(\mathbb{H}^n)=(n-1)^2/4$. Forthese domains, we have comparison principle and some maximum principle.Conversely, for any $s>(n-1)/2,$ we prove the existence of domains withasymptotic boundary of dimension $s$ for which there are bounded$\lambda_1$-harmonic functions that decay exponentially at infinity.

Bounded $\lambda$-harmonic functions in domains of $\mathbb{H}^n$ with asymptotic boundary with fractional dimension