Factoring the Sobolev embedding operator
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913979556691968 |
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| author | Kazaniecki, Krystian Pawlewicz, Aleksander Wojciechowski, Michał |
| author_facet | Kazaniecki, Krystian Pawlewicz, Aleksander Wojciechowski, Michał |
| contents | The paper studies the factorization and summing properties of the Sobolev embedding operator. We propose two different approaches. One shows that the Sobolev embedding operator $S:W^{1,1}(\mathbb{T}^2)\hookrightarrow L_2(\mathbb{T}^2)$ factorises through the identical embedding $\ell_Φ\hookrightarrow\ell_2$ for some Young function with Matuszewska-Orlicz index 1. Proof of this fact is based on two results of independent interest. First, a necessary and sufficient conditions on a Young function $Φ$ and weight $Ψ$ for boundedness of the embedding of the Sobolev space $W^{1,1}(\mathbb{T}^2)$ into Besov-Orlicz space $B^Ψ_{Φ,1}(\mathbb{T}^2)$. Second, a generalization of the Marcinkiewicz sampling theorem to the context of Orlicz spaces. Another approach is based on the extrapolation of $(p,1)$-summing norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Factoring the Sobolev embedding operator Kazaniecki, Krystian Pawlewicz, Aleksander Wojciechowski, Michał Functional Analysis 46E35, 47B10, 30H25 The paper studies the factorization and summing properties of the Sobolev embedding operator. We propose two different approaches. One shows that the Sobolev embedding operator $S:W^{1,1}(\mathbb{T}^2)\hookrightarrow L_2(\mathbb{T}^2)$ factorises through the identical embedding $\ell_Φ\hookrightarrow\ell_2$ for some Young function with Matuszewska-Orlicz index 1. Proof of this fact is based on two results of independent interest. First, a necessary and sufficient conditions on a Young function $Φ$ and weight $Ψ$ for boundedness of the embedding of the Sobolev space $W^{1,1}(\mathbb{T}^2)$ into Besov-Orlicz space $B^Ψ_{Φ,1}(\mathbb{T}^2)$. Second, a generalization of the Marcinkiewicz sampling theorem to the context of Orlicz spaces. Another approach is based on the extrapolation of $(p,1)$-summing norm. |
| title | Factoring the Sobolev embedding operator |
| topic | Functional Analysis 46E35, 47B10, 30H25 |
| url | https://arxiv.org/abs/2503.20478 |