Remark on the Maximum of the Absolute Value of an Analytic Function on the Boundary期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

Remark on the Maximum of the Absolute Value of an Analytic Function on the Boundary

Authors:

N A Shirokov

Institution:

(1) St.Petersburg State University, St.Petersburg, Russia

Abstract:

Let Λ^α be the analytic Holder class in the unit disk $\mathbb{D}$ . For f ∈ Λ^α and $I \subset \partial \mathbb{D}$ , let M_f (I) = max _I |f|. Assume that I and J are arcs such that |J| = 2|I| and J and I have the same midpoint. Then

$M_f \left( J \right) \leqslant C\left( {\alpha ,f} \right)\frac{{\left| I \right|^\alpha + M_f \left( I \right)}}{{\log ^\alpha \left( {\tfrac{{\left| I \right|^\alpha }}{{M_f \left( I \right)}} + 2} \right)}}.$

It is proved that this estimate cannot be improved. Bibliography: 1 title. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 315, 2004, pp. 149–154.

Keywords:

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏