Local dyadic fractional Sobolev spaces: paraproducts, commutators, and the algebra property
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917461912190976 |
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| author | Fragkiadaki, Valentia Mitkovski, Mishko Stockdale, Cody B. |
| author_facet | Fragkiadaki, Valentia Mitkovski, Mishko Stockdale, Cody B. |
| contents | We characterize the boundedness and compactness of dyadic paraproducts on local dyadic fractional Sobolev spaces, $H^s$. We apply this result to establish the algebra property for $H^s$ when $s \in (\frac{1}{2},1)$ and to deduce the boundedness and compactness of commutators with the Haar shift on $H^s$. Our conditions are stated in terms of new dyadic fractional $\text{BMO}^s$ and $\text{CMO}^s$ conditions involving the dyadic fractional Sobolev capacity, and our proof uses a new dyadic fractional version of the Carleson embedding theorem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_26565 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local dyadic fractional Sobolev spaces: paraproducts, commutators, and the algebra property Fragkiadaki, Valentia Mitkovski, Mishko Stockdale, Cody B. Classical Analysis and ODEs 42B20, 42B35, 46E35 We characterize the boundedness and compactness of dyadic paraproducts on local dyadic fractional Sobolev spaces, $H^s$. We apply this result to establish the algebra property for $H^s$ when $s \in (\frac{1}{2},1)$ and to deduce the boundedness and compactness of commutators with the Haar shift on $H^s$. Our conditions are stated in terms of new dyadic fractional $\text{BMO}^s$ and $\text{CMO}^s$ conditions involving the dyadic fractional Sobolev capacity, and our proof uses a new dyadic fractional version of the Carleson embedding theorem. |
| title | Local dyadic fractional Sobolev spaces: paraproducts, commutators, and the algebra property |
| topic | Classical Analysis and ODEs 42B20, 42B35, 46E35 |
| url | https://arxiv.org/abs/2603.26565 |