Dual of the Class of HKr Integrable Functions

被引：0

作者：

Musial, Paul ^{[1
]}

Tulone, Francesco ^{[2
]}

机构：

[1] Chicago Univ, Dept Math & Comp Sci, 9501 S King Dr, Chicago, IL 60628 USA

[2] Palermo Univ, Dept Math & Comp Sci, Viale Sci, I-90128 Palermo, Italy

来源：

MINIMAX THEORY AND ITS APPLICATIONS | 2019年 / 4卷 / 01期

关键词：

L-r-Henstock-Kurzweil integral; HKr-dual; HKr-norm; KURZWEIL-HENSTOCK; RIESZ SPACE; DERIVATIVES; RESPECT;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define for 1 <= r < infinity a norm for the class of functions which are Henstock-Kurzweil integrable in the L-r sense. We then establish that the dual in this norm is isometrically isomorphic to L-r' and is therefore a Banach space, and in the case r = 2, a Hilbert space. Finally, we give results pertaining to convergence and weak convergence in this space.

引用

页码：151 / 160

页数：10

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