Dirichlet级数构成的拓扑线性空间和H￣p空间

TOPOLOGICAL LINEAR SPACE AND Hp SPACE OF FUNCTIONS REPRESENTED BY DIRICHLET SERIES

本文研究了由Ｄｉｒｉｃｈｌｅｔ级数ｆ（ｓ）＝∑∞ｎ＝０ａｎｅ－λｎｓ所构成的拓扑线性空间，并讨论了与其对应的Ｈｐ空间的一些性质，其中０＝λ０＜λｎ↑＋∞，ｌｉｍｎ→∞ｌｏｇｎλｎ＝０，ｌｉｍｎ→∞ｌｏｇ｜ａｎ｜λｎ≤０，ｓ＝σ＋ｉｔ．

Let 0=λ0<λn↑+∞, limn→∞lognλn=0,limn→∞log|an|λn≤0,s=σ+it. In this article we study the linear topological structure of a class of functions represented by Dirichlet series f(s)=∑∞n=0ane-λns. We also discuss some properties of Hp(p≥1) space consisted of Dirichlet series.