dc.contributor.author |
Avkhadiev F. |
|
dc.contributor.author |
Wirths K. |
|
dc.date.accessioned |
2018-09-17T20:27:21Z |
|
dc.date.available |
2018-09-17T20:27:21Z |
|
dc.date.issued |
2001 |
|
dc.identifier.issn |
0024-6093 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/133506 |
|
dc.description.abstract |
Let f be analytic in the unit disc, and let it belong to the Hardy space H p, equipped with the usual norm ∥f∥ p. It is known from the work of Hardy and Littlewood that for q > p, the constants C (p,q) :=sup{∫ 1 0(1 - r) -p/q(1/2π ∫ 2π 0 |f(re iθ)| qdθ) p/qdr|∥f∥ p = 1}, with the usual extension to the case where q = ∞, have C(p,q) < ∞. The authors prove that lim q→p( - p/q)C(p,q) = 1, inf p<q≤∞ (1 - p/q)C(p,q) = 1 and max p<q≤∞ (1 - p/q)C(p, q) = C(p, ∞) = π. |
|
dc.relation.ispartofseries |
Bulletin of the London Mathematical Society |
|
dc.title |
Asymptotically sharp bounds in the Hardy-Littlewood inequalities on mean values of analytic functions |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
6 |
|
dc.relation.ispartofseries-volume |
33 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
695 |
|
dc.source.id |
SCOPUS00246093-2001-33-6-SID0035513328 |
|