A sufficient condition for Haar multipliers in Triebel-Lizorkin spaces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866918104946180096 |
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| author | Garrigós, Gustavo Seeger, Andreas Ullrich, Tino |
| author_facet | Garrigós, Gustavo Seeger, Andreas Ullrich, Tino |
| contents | We consider Haar multiplier operators $T_m$ acting on Sobolev spaces, and more generally Triebel-Lizorkin spaces $F^s_{p,q}(\mathbb{R})$, for indices in which the Haar system is not unconditional. When $m$ depends only on the Haar frequency, we give a sufficient condition for the boundedness of $T_m$ in $F^s_{p,q}$, in terms of the variation norms $\|m\|_{V_u}$, which is optimal in $u$ (up to endpoints) when $p, q> 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11906 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A sufficient condition for Haar multipliers in Triebel-Lizorkin spaces Garrigós, Gustavo Seeger, Andreas Ullrich, Tino Classical Analysis and ODEs 46E35, 46B15, 42C40 We consider Haar multiplier operators $T_m$ acting on Sobolev spaces, and more generally Triebel-Lizorkin spaces $F^s_{p,q}(\mathbb{R})$, for indices in which the Haar system is not unconditional. When $m$ depends only on the Haar frequency, we give a sufficient condition for the boundedness of $T_m$ in $F^s_{p,q}$, in terms of the variation norms $\|m\|_{V_u}$, which is optimal in $u$ (up to endpoints) when $p, q> 1$. |
| title | A sufficient condition for Haar multipliers in Triebel-Lizorkin spaces |
| topic | Classical Analysis and ODEs 46E35, 46B15, 42C40 |
| url | https://arxiv.org/abs/2301.11906 |