Precompactness in bivariate metric semigroup-valued bounded variation spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912177786454016 |
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| author | Xu, Jingshi Niu, Yinglian |
| author_facet | Xu, Jingshi Niu, Yinglian |
| contents | In this paper, we show that if a set in bivariate metric semigroups-valued bounded variation spaces is pointwise totally bounded and joint equivariated then it is precompact. These spaces include bounded Jordan variation spaces, bounded Wiener variation spaces, bounded Waterman variation spaces, bounded Riesz variation spaces and bounded Korenblum variation spaces. To do so, we introduce the concept of equimetric set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Precompactness in bivariate metric semigroup-valued bounded variation spaces Xu, Jingshi Niu, Yinglian Functional Analysis 26A45, 54E50 In this paper, we show that if a set in bivariate metric semigroups-valued bounded variation spaces is pointwise totally bounded and joint equivariated then it is precompact. These spaces include bounded Jordan variation spaces, bounded Wiener variation spaces, bounded Waterman variation spaces, bounded Riesz variation spaces and bounded Korenblum variation spaces. To do so, we introduce the concept of equimetric set. |
| title | Precompactness in bivariate metric semigroup-valued bounded variation spaces |
| topic | Functional Analysis 26A45, 54E50 |
| url | https://arxiv.org/abs/2501.02528 |