| Title:
|
Mean values and associated measures of $\delta $-subharmonic functions (English) |
| Author:
|
Watson, Neil A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
83-102 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $u$ be a $\delta $-subharmonic function with associated measure $\mu $, and let $v$ be a superharmonic function with associated measure $\nu $, on an open set $E$. For any closed ball $B(x,r)$, of centre $x$ and radius $r$, contained in $E$, let ${\mathcal M}(u,x,r)$ denote the mean value of $u$ over the surface of the ball. We prove that the upper and lower limits as $s,t\rightarrow 0$ with $0<s<t$ of the quotient $({\mathcal M}(u,x,s)-{\mathcal M}(u,x,t))/({\mathcal M}(v,x,s)-{\mathcal M}(v,x,t))$, lie between the upper and lower limits as $r\rightarrow 0+$ of the quotient $\mu (B(x,r))/\nu (B(x,r))$. This enables us to use some well-known measure-theoretic results to prove new variants and generalizations of several theorems about $\delta $-subharmonic functions. (English) |
| Keyword:
|
superharmonic |
| Keyword:
|
$\delta $-subharmonic |
| Keyword:
|
Riesz measure |
| Keyword:
|
spherical mean values |
| MSC:
|
31B05 |
| idZBL:
|
Zbl 0998.31002 |
| idMR:
|
MR1895249 |
| DOI:
|
10.21136/MB.2002.133981 |
| . |
| Date available:
|
2009-09-24T21:58:22Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133981 |
| . |
| Reference:
|
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| . |
