Exact estimates for integrals involving Dirichlet series with nonnegative coefficients

被引：1

作者：

Móricz, F ^{[1
]}

机构：

[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1999年 / 127卷 / 08期

关键词：

Dirichlet series; power series; Cauchy-Hadamard criterion for Dirichlet series; line of convergence; L-p-behavior; weight function; slowly decreasing function; Cauchy condensation principle;

D O I：

10.1090/S0002-9939-99-04851-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Dirichlet series [GRAPHICS] with coefficients a(k) greater than or equal to 0 for all k. Among others, we prove exact estimates of certain weighted L-p -norms of f on the unit interval (0, 1) for any 0 < p < infinity, in terms of the coefficients a(k). Our estimation is based on the close relationship between Dirichlet series and power series. This enables us to derive exact estimates for integrals involving the former one by relying on exact estimates for integrals involving the latter one. As a by-product, we obtain an analogue of the Cauchy-Hadamard criterion of (absolute) convergence of the more general Dirichlet series [GRAPHICS] with complex coefficients c(k).

引用

页码：2417 / 2422

页数：6