A new characterization of the dual space of Henstock–Kurzweil integrable functions over $\mathbb {R}$

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2025年3月11日

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Juan H. Arredondo,
Genaro Montaño-Morales,
Francisco J. Mendoza

摘要

Recently we have shown in a previous article a full characterization of the dual space of the Henstock–Kurzweil integrable function over a bounded interval. In this manuscript we construct the Henstock–Kurzweil integral over $\mathbb {R}$ $R$ as an extension of a linear form initially defined on the classical space $L^1(\mathbb {R})$ $L^{1} (R)$ . In particular, we give a full characterization of the dual space of Henstock–Kurzweil integrable functions over $\mathbb {R}$ $R$ in terms of a quotient space. Furthermore, the non-reflexivity of these spaces is also shown.

A new characterization of the dual space of Henstock–Kurzweil integrable functions over \(\mathbb {R}\)

摘要