dc.contributor.author |
Kayumov I. |
|
dc.date.accessioned |
2018-09-17T20:03:51Z |
|
dc.date.available |
2018-09-17T20:03:51Z |
|
dc.date.issued |
2004 |
|
dc.identifier.issn |
0001-4346 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/132979 |
|
dc.description.abstract |
In this paper, the following sharp estimate is proved: ∫ 0 2π|F′(e iθ)| p, dθ ≤ √π2 1+pΓ(1/2+p/2)/Γ(1+p/2)}, p>-1, where F is the conformal mapping of the domain D - = {ζ:|ζ| > 1} onto the exterior of a convex curve, with F'(\infty)=\nomathbreak 1. For p=\nomathbreak 1, this result is due to Pólya and Shiffer. We also obtain several generalizations of this estimate under other geometric assumptions about the structure of the domain F(D -). |
|
dc.relation.ispartofseries |
Mathematical Notes |
|
dc.subject |
analytic univalent function |
|
dc.subject |
conformal mapping |
|
dc.subject |
estimates for integral means |
|
dc.subject |
Euler beta function |
|
dc.subject |
harmonic function |
|
dc.subject |
Joukowski function |
|
dc.title |
Sharp estimates for integral means for three classes of domains |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
3-4 |
|
dc.relation.ispartofseries-volume |
76 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
472 |
|
dc.source.id |
SCOPUS00014346-2004-76-34-SID5044237578 |
|