A Marcinkiewicz-Zygmund inequality and the Kadec Pełczynśki theorem in Orlicz spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917336864260096 |
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| author | Berkes, Istvan Stefanescu, Eduard Tichy, Robert |
| author_facet | Berkes, Istvan Stefanescu, Eduard Tichy, Robert |
| contents | In this paper, we extend the Marcinkiewicz--Zygmund inequality to the setting of Orlicz and Lorentz spaces. Furthermore, we generalize a Kadec--Pełczyński-type result -- originally established by the first and third authors for $L^p$ spaces with $1 \le p < 2$ -- to a broader class of Orlicz spaces defined via Young functions $ψ$ satisfying $x \le ψ(x) \le x^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Marcinkiewicz-Zygmund inequality and the Kadec Pełczynśki theorem in Orlicz spaces Berkes, Istvan Stefanescu, Eduard Tichy, Robert Functional Analysis Probability In this paper, we extend the Marcinkiewicz--Zygmund inequality to the setting of Orlicz and Lorentz spaces. Furthermore, we generalize a Kadec--Pełczyński-type result -- originally established by the first and third authors for $L^p$ spaces with $1 \le p < 2$ -- to a broader class of Orlicz spaces defined via Young functions $ψ$ satisfying $x \le ψ(x) \le x^2$. |
| title | A Marcinkiewicz-Zygmund inequality and the Kadec Pełczynśki theorem in Orlicz spaces |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2506.04025 |