THE SUPPORT POINTS AND EXTREME POINTS OF THE UNIT BALL OF H'_P~ 1

By the author denotes the areal measure on the unit disk . Let H'p = {f(z): f(z) is analytic in D and . Let B H 'p and. This article researches the support points and extreme points of B(H'p).

EXTREME POINTS AND SUPPORT POINTS OF A CLASS OF ANALYTIC FUNCTIONS

Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infinity) b(n)a(n) less than or equal to 1 and Sigma(n=2)(+infinity) c(n)a(n) less than or equal to 1}. This article obtains the extreme points and support points of F({b(n)}, {c(n)}).

一类单叶调和函数族的极值点与支撑点

设T是由具有形式f(z)=z-∑+∞n=2anzn-∑+∞n=2bnz-n,且满足条件an≥0,bn≥0,∑+∞n=2n(an+bn)≤1的所有复值调和函数组成的函数族.找出了函数族T的极值点与支撑点.

星形函数族的一个子族的极值点与支撑点(英文)

设Ｆ（｛ｎ｝）＝｛ｆ（ｚ）：ｆ（ｚ）在｜ｚ｜＜１内解析，ｆ（ｚ）＝ｚ－∞ｎ＝１ａｎｚｎ，ａｎ≥０，＋∞ｎ＝２ｎａｎ≤１｝，则Ｆ（｛ｎ｝）是星形函数族的一个子族．许多学者研究了这个函数族．设Ｍ＝｛ｆ（ｚ）：ｆ（ｚ）在｜ｚ｜＜１内解析，ｆ（ｚ）＝ｚ－∞ｎ＝１ａｎｚｎ，ａｎ≥ａｎ＋１≥０，＋∞ｎ＝２ｎａｎ≤１｝．在本文中我们找出了函数族Ｍ的极值点与支撑点．

一类解析函数族的极值点与支撑点

设Ｇ＝｛ｆ（ｚ）：ｆ（ｚ）在｜ｚ｜＜１上解析，ｆ（ｚ）＝ｚ－∑∞ｎ＝２ａｎｚｎ，ａｎ≥０，∑∞ｎ＝２ｎａｎ≤１，∑∞ｎ＝３ｎ（ｎ－１）ａｎ≤２ａ２｝．本文找出了函数族Ｇ的极值点与支撑点．