# Quasi-nearly subharmonic functions in locally uniformly homogeneous spaces

Quasi-nearly subharmonic functions in locally uniformly homogeneous spaces We define nonnegative quasi-nearly subharmonic functions on so called locally uniformly homogeneous spaces. We point out that this function class is rather general. It includes quasi-nearly subharmonic (thus also subharmonic, quasisubharmonic and nearly subharmonic) functions on domains of Euclidean spaces $${{\mathbb{R}}^n}$$ , n ≥ 2. In addition, quasi-nearly subharmonic functions with respect to various measures on domains of $${{\mathbb{R}}^n}$$ , n ≥ 2, are included. As examples we list the cases of the hyperbolic measure on the unit ball B n of $${{\mathbb{R}}^n}$$ , the $${{\mathcal{M}}}$$ -invariant measure on the unit ball B 2n of $${{\mathbb{C}}^n}$$ , n ≥ 1, and the quasihyperbolic measure on any domain $${D\subset {\mathbb{R}}^n}$$ , $${D\ne {\mathbb{R}}^n}$$ . Moreover, we show that if u is a quasi-nearly subharmonic function on a locally uniformly homogeneous space and the space satisfies a mild additional condition, then also u p is quasi-nearly subharmonic for all p > 0. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Quasi-nearly subharmonic functions in locally uniformly homogeneous spaces

10 pages

/lp/springer-journals/quasi-nearly-subharmonic-functions-in-locally-uniformly-homogeneous-IYKwyoG5uj
Publisher site
See Article on Publisher Site

### Abstract

We define nonnegative quasi-nearly subharmonic functions on so called locally uniformly homogeneous spaces. We point out that this function class is rather general. It includes quasi-nearly subharmonic (thus also subharmonic, quasisubharmonic and nearly subharmonic) functions on domains of Euclidean spaces $${{\mathbb{R}}^n}$$ , n ≥ 2. In addition, quasi-nearly subharmonic functions with respect to various measures on domains of $${{\mathbb{R}}^n}$$ , n ≥ 2, are included. As examples we list the cases of the hyperbolic measure on the unit ball B n of $${{\mathbb{R}}^n}$$ , the $${{\mathcal{M}}}$$ -invariant measure on the unit ball B 2n of $${{\mathbb{C}}^n}$$ , n ≥ 1, and the quasihyperbolic measure on any domain $${D\subset {\mathbb{R}}^n}$$ , $${D\ne {\mathbb{R}}^n}$$ . Moreover, we show that if u is a quasi-nearly subharmonic function on a locally uniformly homogeneous space and the space satisfies a mild additional condition, then also u p is quasi-nearly subharmonic for all p > 0.

### Journal

PositivitySpringer Journals

Published: Nov 25, 2009

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create folders to

Export folders, citations