Approximation via partial Hausdorff integrals on $H^1(\mathbb{R})$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915650417459200 |
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| author | Yu, Zifei Li, Baode |
| author_facet | Yu, Zifei Li, Baode |
| contents | We obtain the result of approximating \( f \) in the \( H^1(\mathbb{R}) \) norm using partial Hausdorff integrals. Specifically, by leveraging the homogeneous multiplier theory of \( H^1(\mathbb{R}) \) and the \( K \) functional theory, one result from Pinos and Liflyand [CMB,~2021,~64,~no.3] is extended from \( L^p(\mathbb{R}) \) ( \( 1 \leq p \leq \infty \)) to \( H^1(\mathbb{R}) \). As applications, four examples of partial Hausdorff integrals are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation via partial Hausdorff integrals on $H^1(\mathbb{R})$ Yu, Zifei Li, Baode Classical Analysis and ODEs 41A25 We obtain the result of approximating \( f \) in the \( H^1(\mathbb{R}) \) norm using partial Hausdorff integrals. Specifically, by leveraging the homogeneous multiplier theory of \( H^1(\mathbb{R}) \) and the \( K \) functional theory, one result from Pinos and Liflyand [CMB,~2021,~64,~no.3] is extended from \( L^p(\mathbb{R}) \) ( \( 1 \leq p \leq \infty \)) to \( H^1(\mathbb{R}) \). As applications, four examples of partial Hausdorff integrals are also given. |
| title | Approximation via partial Hausdorff integrals on $H^1(\mathbb{R})$ |
| topic | Classical Analysis and ODEs 41A25 |
| url | https://arxiv.org/abs/2511.11312 |