Krzysztof Ostaszewski, "The space of Henstock integrable functions of two variables", International Journal of Mathematics and Mathematical Sciences, vol. 11, Article ID 428978, 7 pages, 1988. https://doi.org/10.1155/S0161171288000043
The space of Henstock integrable functions of two variables
We consider the space of Henstock integrable functions of two variables. Equipped with the Alexiewicz norm the space is proved to be barrelled. We give a partial description of its dual. We show by an example that the dual can't be described in a manner analogous to the one-dimensional case, since in two variables there exist functions whose distributional partials are measures and which are not multipliers for Henstock integrable functions.
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