Abstract
In this paper, we give criteria for the relatively compact sets of Banach space-valued bounded-variation spaces in the sense of Jordan and Banach space-valued bounded Wiener p-variation spaces as \(p\in (0,1)\). Then, we give sufficient conditions for the relatively compact sets of others Banach space-valued bounded variation spaces, such as Banach space-valued bounded Wiener p-variation spaces as \(p\in (1,\infty )\), Banach space-valued bounded Wiener–Young variation spaces, Banach space-valued bounded Schramm variation spaces, Banach space-valued bounded Waterman variation spaces, Banach space-valued bounded Riesz variation spaces, and Banach space-valued bounded Korenblum variation spaces.
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Acknowledgements
The authors would like to thank the referees for their suggestions. Jingshi Xu is partially supported by the National Natural Science Foundation of China (Grant No. 12161022) and Guangxi Natural Science Foundation (Grant No. 2020GXNSFAA159085).
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Communicated by Dachun YANG.
Dedicated to the memory of my brother Jingyou Xu.
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Si, Y., Xu, J. Relatively compact sets of Banach space-valued bounded-variation spaces. Banach J. Math. Anal. 17, 7 (2023). https://doi.org/10.1007/s43037-022-00230-5
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DOI: https://doi.org/10.1007/s43037-022-00230-5