Multilinear paraproducts on Sobolev spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910494414077952 |
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| author | Di Plinio, Francesco Green, A. Walton Wick, Brett D. |
| author_facet | Di Plinio, Francesco Green, A. Walton Wick, Brett D. |
| contents | Paraproducts are a special subclass of the multilinear Calderón-Zygmund operators, and their Lebesgue space estimates in the full multilinear range are characterized by the $\mathrm{BMO}$ norm of the symbol. In this note, we characterize the Sobolev space boundedness properties of multilinear paraproducts in terms of a suitable family of Triebel-Lizorkin type norms of the symbol. Coupled with a suitable wavelet representation theorem, this characterization leads to a new family of Sobolev space $T(1)$-type theorems for multilinear Calderón-Zygmund operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_13174 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multilinear paraproducts on Sobolev spaces Di Plinio, Francesco Green, A. Walton Wick, Brett D. Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B20 Paraproducts are a special subclass of the multilinear Calderón-Zygmund operators, and their Lebesgue space estimates in the full multilinear range are characterized by the $\mathrm{BMO}$ norm of the symbol. In this note, we characterize the Sobolev space boundedness properties of multilinear paraproducts in terms of a suitable family of Triebel-Lizorkin type norms of the symbol. Coupled with a suitable wavelet representation theorem, this characterization leads to a new family of Sobolev space $T(1)$-type theorems for multilinear Calderón-Zygmund operators. |
| title | Multilinear paraproducts on Sobolev spaces |
| topic | Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B20 |
| url | https://arxiv.org/abs/2406.13174 |