The spaces of functions of finite upper 𝑝-variation

Nelson, Robert R.

doi:10.1090/S0002-9947-1979-0536941-8

The spaces of functions of finite upper $p$-variation
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by Robert R. Nelson PDF

Trans. Amer. Math. Soc. 253 (1979), 171-190 Request permission

Abstract:

Let y be a Banach space, $1 \leqslant p < \infty$, and ${U_p}$ be the semi-normed space of Y-valued Bochner measurable functions of a real variable which have finite upper p-variation. Let ${\tilde U_p}$ be the space of ${U_p}$-equivalence classes. An averaging operator is defined with the aid of the theory of helixes in Banach spaces, which enables us to show that the spaces ${\tilde U_p}$ are Banach spaces, to characterize their members, and to show that they are isometrically isomorphic to Banach spaces of Y-valued measures with bounded p-variation.

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The completeness of the class of functions of bounded upper p-variation

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