ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONS
The classical theorem of growth regularity in the class S of analytic and univalent in the unit disc ∆ functions ƒ describes the growth character of different functionals of ƒ Є S and z Є ∆ as z tends to δ∆. Earlier the authors proved the theorems of growth and decrease regularity for harmonic and s...
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Petrozavodsk State University
2015-05-01
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| Series: | Проблемы анализа |
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| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=2910&lang=en |
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doaj-068a2e6a25624af68b33e1b5b96878182021-07-02T14:43:57ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322015-05-01422385610.15393/j3.art.2015.2910ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONSE. G. Ganenkova0V. V. Starkov1Petrozavodsk State UniversityPetrozavodsk State UniversityThe classical theorem of growth regularity in the class S of analytic and univalent in the unit disc ∆ functions ƒ describes the growth character of different functionals of ƒ Є S and z Є ∆ as z tends to δ∆. Earlier the authors proved the theorems of growth and decrease regularity for harmonic and sense-preserving in ∆ functions which generalized the classical result for the class S. In the presented paper we establish new properties of harmonic sense-preserving functions, connected with the regularity theorems. The effects both common for analytic and harmonic case and specific for harmonic functions are displayed.http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=2910&lang=enregularity theoremlinearly invariant familyharmonic function |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
E. G. Ganenkova V. V. Starkov |
| spellingShingle |
E. G. Ganenkova V. V. Starkov ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONS Проблемы анализа regularity theorem linearly invariant family harmonic function |
| author_facet |
E. G. Ganenkova V. V. Starkov |
| author_sort |
E. G. Ganenkova |
| title |
ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONS |
| title_short |
ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONS |
| title_full |
ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONS |
| title_fullStr |
ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONS |
| title_full_unstemmed |
ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONS |
| title_sort |
on regularity theorems for linearly invariant families of harmonic functions |
| publisher |
Petrozavodsk State University |
| series |
Проблемы анализа |
| issn |
2306-3424 2306-3432 |
| publishDate |
2015-05-01 |
| description |
The classical theorem of growth regularity in the class S of analytic and univalent in the unit disc ∆ functions ƒ describes the growth character of different functionals of ƒ Є S and z Є ∆ as z tends to δ∆. Earlier the authors proved the theorems of growth and decrease regularity for harmonic and sense-preserving in ∆ functions which generalized the classical result for the class S. In the presented paper we establish new properties of harmonic sense-preserving functions, connected with the regularity theorems. The effects both common for analytic and harmonic case and specific for harmonic functions are displayed. |
| topic |
regularity theorem linearly invariant family harmonic function |
| url |
http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=2910&lang=en |
| work_keys_str_mv |
AT egganenkova onregularitytheoremsforlinearlyinvariantfamiliesofharmonicfunctions AT vvstarkov onregularitytheoremsforlinearlyinvariantfamiliesofharmonicfunctions |
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1721327653788581888 |