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
收藏
页码：151 / 160
页数：10
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