| Title:
|
On the asymptotics of counting functions for Ahlfors regular sets (English) |
| Author:
|
Pokorný, Dušan |
| Author:
|
Rauch, Marc |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
63 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
69-119 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deal with the so-called Ahlfors regular sets (also known as $s$-regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: Under which conditions does the limit $\lim_{\varepsilon\to 0+} \varepsilon^s N(\varepsilon,K)$ exist, where $K$ is an $s$-regular set and $N(\varepsilon,K)$ is for instance the $\varepsilon$-packing number of $K$? (English) |
| Keyword:
|
Ahlfors regular |
| Keyword:
|
$s$-regular |
| Keyword:
|
packing number |
| Keyword:
|
Minkowski measurability |
| Keyword:
|
renewal theory |
| MSC:
|
28A80 |
| MSC:
|
30L99 |
| idZBL:
|
Zbl 07584114 |
| idMR:
|
MR4445738 |
| DOI:
|
10.14712/1213-7243.2022.011 |
| . |
| Date available:
|
2022-07-18T11:52:08Z |
| Last updated:
|
2024-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150429 |
| . |
| Reference:
|
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