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Equivalence of the local Markov inequality and a Kolmogorov type inequality in the complex plane
Journal
Potential Analysis
40
Author
Białas-Cież Leokadia
Eggink Raimondo
Volume
38
Issue
1
Pages
299-317
ISSN
0926-2601
eISSN
1572-929X
Keywords in English
Markov inequality
Kolmogorov inequality
Green function
L-regularity of sets
Holomorphic functions
Cantor sets
Language
English
Container language
English
Abstract in English
We prove that a compact subset of the complex plane satisfies a local Markov inequality if and only if it satisfies a Kolmogorov type inequality. This result generalizes a theorem established by Bos and Milman in the real case. We also show that every set satisfying the local Markov inequality is a sum of Cantor type sets which are regular in the sense of the potential theory.
Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
WoS citations
4
| cris.lastimport.scopus | 2024-04-07T17:57:12Z | |
| cris.lastimport.wos | 2024-04-10T00:35:09Z | |
| dc.abstract.en | We prove that a compact subset of the complex plane satisfies a local Markov inequality if and only if it satisfies a Kolmogorov type inequality. This result generalizes a theorem established by Bos and Milman in the real case. We also show that every set satisfying the local Markov inequality is a sum of Cantor type sets which are regular in the sense of the potential theory. | pl |
| dc.affiliation | Wydział Matematyki i Informatyki : Instytut Matematyki | pl |
| dc.contributor.author | Białas-Cież, Leokadia - 127297 | pl |
| dc.contributor.author | Eggink, Raimondo | pl |
| dc.date.accessioned | 2014-07-15T05:31:14Z | |
| dc.date.available | 2014-07-15T05:31:14Z | |
| dc.date.issued | 2013 | pl |
| dc.date.openaccess | 0 | |
| dc.description.accesstime | w momencie opublikowania | |
| dc.description.number | 1 | pl |
| dc.description.physical | 299-317 | pl |
| dc.description.version | ostateczna wersja wydawcy | |
| dc.description.volume | 38 | pl |
| dc.identifier.doi | 10.1007/s11118-012-9274-0 | pl |
| dc.identifier.eissn | 1572-929X | pl |
| dc.identifier.issn | 0926-2601 | pl |
| dc.identifier.uri | http://ruj.uj.edu.pl/xmlui/handle/item/20 | |
| dc.language | eng | pl |
| dc.language.container | eng | pl |
| dc.rights | * | |
| dc.rights.licence | CC-BY | |
| dc.rights.uri | * | |
| dc.share.type | inne | |
| dc.subject.en | Markov inequality | pl |
| dc.subject.en | Kolmogorov inequality | pl |
| dc.subject.en | Green function | pl |
| dc.subject.en | L-regularity of sets | pl |
| dc.subject.en | Holomorphic functions | pl |
| dc.subject.en | Cantor sets | pl |
| dc.subtype | Article | pl |
| dc.title | Equivalence of the local Markov inequality and a Kolmogorov type inequality in the complex plane | pl |
| dc.title.journal | Potential Analysis | pl |
| dc.type | JournalArticle | pl |
| dspace.entity.type | Publication |