Bourgain's method for K-closedness in the semicommmutative setting
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917438686232576 |
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| author | Moyart, Hugues |
| author_facet | Moyart, Hugues |
| contents | In the early 1990s, J.Bourgain proved a general result $K$-closedness result in the context of classical harmonic analysis. In this paper, we extend Bourgain's method to the semicommutative setting, making use of the recent semicommutative Calderón-Zygmund decomposition introduced by L.Cadilhac, JM.Conde-Alonso and J.Parcet. As an application, we recover Pisier's result about $K$-closedness of noncommutative Hardy spaces on the torus, and we also establish new interpolation results for noncommutative Sobolev spaces on the torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23864 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bourgain's method for K-closedness in the semicommmutative setting Moyart, Hugues Functional Analysis Operator Algebras In the early 1990s, J.Bourgain proved a general result $K$-closedness result in the context of classical harmonic analysis. In this paper, we extend Bourgain's method to the semicommutative setting, making use of the recent semicommutative Calderón-Zygmund decomposition introduced by L.Cadilhac, JM.Conde-Alonso and J.Parcet. As an application, we recover Pisier's result about $K$-closedness of noncommutative Hardy spaces on the torus, and we also establish new interpolation results for noncommutative Sobolev spaces on the torus. |
| title | Bourgain's method for K-closedness in the semicommmutative setting |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2604.23864 |