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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.01092 |
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| _version_ | 1866910184927920128 |
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| author | Rocha, Pablo |
| author_facet | Rocha, Pablo |
| contents | For $0 \leq α< n$ and $m \in \mathbb{N} \cap \left(1 - \fracα{n}, +\infty \right)$, we consider certain fractional type operators $T_{α, m}$ generated by $m$-orthogonal matrices and prove that, for $0 < α< n$, $T_{α, m}$ can be extended to a bounded operator $H_X \to Y$ and, for $α= 0$, $T_{0, m}$ can be extended to a bounded operator $H_X \to X$, where $X$ and $Y$ are certain ball quasi-Banach spaces related to each other and $H_X$ is the Hardy space associated with $X$. In particular, our results apply to weighted Lebesgue spaces, variable Lebesgue spaces, Lorentz spaces and Orlicz spaces, the last two are new. Our proofs rely on the ssumption that $X$ is $\mathcal{O}(n)$-invariant, the theory of weighted Hardy spaces, the Rubio de Francia iteration algorithm and the finite atomic decomposition of $H_X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01092 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fractional type operators on Hardy spaces associated with ball quasi-Banach function spaces Rocha, Pablo Functional Analysis For $0 \leq α< n$ and $m \in \mathbb{N} \cap \left(1 - \fracα{n}, +\infty \right)$, we consider certain fractional type operators $T_{α, m}$ generated by $m$-orthogonal matrices and prove that, for $0 < α< n$, $T_{α, m}$ can be extended to a bounded operator $H_X \to Y$ and, for $α= 0$, $T_{0, m}$ can be extended to a bounded operator $H_X \to X$, where $X$ and $Y$ are certain ball quasi-Banach spaces related to each other and $H_X$ is the Hardy space associated with $X$. In particular, our results apply to weighted Lebesgue spaces, variable Lebesgue spaces, Lorentz spaces and Orlicz spaces, the last two are new. Our proofs rely on the ssumption that $X$ is $\mathcal{O}(n)$-invariant, the theory of weighted Hardy spaces, the Rubio de Francia iteration algorithm and the finite atomic decomposition of $H_X$. |
| title | Fractional type operators on Hardy spaces associated with ball quasi-Banach function spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2605.01092 |