Embeddability of $\ell_p$-spaces into mixed-norm Lebesgue spaces in connection with the validity of vector-valued extensions of the Riesz--Fischer Theorem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909519597010944 |
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| author | Ansorena, José L. Bello, Glenier |
| author_facet | Ansorena, José L. Bello, Glenier |
| contents | The aim of this paper is twofold. On the one hand, we compute, in terms of $r$ and $s$, the indices $p$ for which $\ell_p$ isomorphically embeds into the mixed-norm separable spaces $L_s(L_r)$, $\ell_s(L_r)$, $L_s(\ell_r)$ and $\ell_s(\ell_r)$. On the other hand, we use this information to move forward in the isomorphic classification of mixed-norm spaces. In particular, we tell apart the spaces $L_2(L_r)$ and $\ell_2(L_r)$, $r\not=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13561 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embeddability of $\ell_p$-spaces into mixed-norm Lebesgue spaces in connection with the validity of vector-valued extensions of the Riesz--Fischer Theorem Ansorena, José L. Bello, Glenier Functional Analysis The aim of this paper is twofold. On the one hand, we compute, in terms of $r$ and $s$, the indices $p$ for which $\ell_p$ isomorphically embeds into the mixed-norm separable spaces $L_s(L_r)$, $\ell_s(L_r)$, $L_s(\ell_r)$ and $\ell_s(\ell_r)$. On the other hand, we use this information to move forward in the isomorphic classification of mixed-norm spaces. In particular, we tell apart the spaces $L_2(L_r)$ and $\ell_2(L_r)$, $r\not=2$. |
| title | Embeddability of $\ell_p$-spaces into mixed-norm Lebesgue spaces in connection with the validity of vector-valued extensions of the Riesz--Fischer Theorem |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2502.13561 |