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arXiv · 2201.11537

On the generalized Wiener bounded variation spaces with p-variable

Ani Ozbetelashvili·Shalva Zviadadze
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Abstract

In this paper, we have investigated the generalized Wiener space of bounded variation with $p$-variable. Various results are obtained such as uniform convexity and reflexivity, there was characterized the set of points of discontinuity of functions from this space. For bounded exponents, it is shown the existence of right and left-hand limits in each point. Also, there is an unbounded exponent such that in corresponding generalized Wiener bounded variation space exists a function that does not have the right-hand limit at a point. Also, for some wide classes of exponents in this space additivity of the variation is not fulfilled.

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Ani Ozbetelashvili, Shalva Zviadadze. 2022-01-27. On the generalized Wiener bounded variation spaces with p-variable. https://arxiv.org/abs/2201.11537

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