Factorization in independent sums of Haar system Hardy spaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915408413458432 |
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| author | Konstantos, Konstantinos Speckhofer, Thomas |
| author_facet | Konstantos, Konstantinos Speckhofer, Thomas |
| contents | We introduce a generalization of the Bourgain-Rosenthal-Schechtman $R_ω^p$ space: Let $Y$ be a Haar system Hardy space, i.e., a separable rearrangement-invariant function space on the unit interval or an associated Hardy space defined via the square function (such as dyadic $H^1$). Then we define $Y_ω$ as the closed linear span in $Y$ of independent distributional copies of the spaces $Y_n$ of dyadic step functions at scale $2^{-n}$. Combining finite-dimensional and infinite-dimensional techniques, we prove that the identity operator $I$ on $Y_ω$ factors through every bounded linear operator $T$ on $Y_ω$ which has large diagonal, and in general, the identity factors either through $T$ or through $I - T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Factorization in independent sums of Haar system Hardy spaces Konstantos, Konstantinos Speckhofer, Thomas Functional Analysis 46B25, 46B09, 47A68, 47L20, 46E30, 30H10 We introduce a generalization of the Bourgain-Rosenthal-Schechtman $R_ω^p$ space: Let $Y$ be a Haar system Hardy space, i.e., a separable rearrangement-invariant function space on the unit interval or an associated Hardy space defined via the square function (such as dyadic $H^1$). Then we define $Y_ω$ as the closed linear span in $Y$ of independent distributional copies of the spaces $Y_n$ of dyadic step functions at scale $2^{-n}$. Combining finite-dimensional and infinite-dimensional techniques, we prove that the identity operator $I$ on $Y_ω$ factors through every bounded linear operator $T$ on $Y_ω$ which has large diagonal, and in general, the identity factors either through $T$ or through $I - T$. |
| title | Factorization in independent sums of Haar system Hardy spaces |
| topic | Functional Analysis 46B25, 46B09, 47A68, 47L20, 46E30, 30H10 |
| url | https://arxiv.org/abs/2507.18600 |