INTEGRAL MEANS OF DERIVATIVES OF UNIVALENT FUNCTIONS IN HARDY SPACES

被引：0

作者：

Perez-Gonzalez, Fernando ^{[1
,2
]}

Rattya, Jouni ^{[3
]}

Vesikko, Toni ^{[3
]}

机构：

[1] Univ La Laguna, Dept Anal Matemat, POB 456, Tenerife 38200, Spain

[2] Univ La Laguna, Inst Matemat & Aplicac IMAULL, POB 456, Tenerife 38200, Spain

[3] Univ Eastern Finland, POB 111, Joensuu 80101, Finland

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 02期

关键词：

Hardy space; integral mean; univalent function; close-to-convex function;

D O I：

10.1090/proc/16132

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the norm in the Hardy space H-p satisfies (dagger) parallel to f parallel to(p)(Hp) (sic) integral(1)(0) M-q(p)(r, f')(1 - r)(p(1-1/q)) dr + vertical bar f(0)vertical bar(p) for all univalent functions provided that either q >= 2 or 2p/2+p < q < 2. This asymptotic was previously known in the cases 0 < p <= q < infinity and p/1+p < q < p < 2 + 2/157 by results due to Pommerenke [Math. Ann. 145 (1961/62), pp. 285-296], Baernstein, Girela and Pelaez [Illinois J. Math. 48 (2004), pp. 837-859] and Gonzalez and Pelaez [J. Geom. Anal. 19 (2009), pp. 755-771]. It is also shown that (dagger) is satisfied for all close-to-convex functions if 1 <= q < infinity. A counterpart of (dagger) in the setting of weighted Bergman spaces is also briefly discussed.

引用

页码：611 / 621

页数：11

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