The nonlinear estimates on quantum Besov spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909038775631872 |
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| author | Chen, Deyu Hong, Guixiang |
| author_facet | Chen, Deyu Hong, Guixiang |
| contents | The superposition operators have been widely studied in nonlinear analysis, which are essential for the well-posedness theory of nonlinear equations. In this paper, we investigate the boundedness estimates of superposition operators with non-smooth symbols on quantum Besov spaces, which significantly generalize McDonald's results \cite{McNLE} for infinitely differentiable symbols and have rich applications in the well-posedness theory of noncommutative PDEs. The ingredients in the proof involve a novel quantum chain rule and nonlinear interpolation. As a byproduct, we prove the equivalence of the two descriptions of quantum Besov spaces, resolving the conjecture proposed in \cite[Remark 3.16]{McNLE}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11934 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The nonlinear estimates on quantum Besov spaces Chen, Deyu Hong, Guixiang Functional Analysis Analysis of PDEs 46L52, 42B37, 35Q30 The superposition operators have been widely studied in nonlinear analysis, which are essential for the well-posedness theory of nonlinear equations. In this paper, we investigate the boundedness estimates of superposition operators with non-smooth symbols on quantum Besov spaces, which significantly generalize McDonald's results \cite{McNLE} for infinitely differentiable symbols and have rich applications in the well-posedness theory of noncommutative PDEs. The ingredients in the proof involve a novel quantum chain rule and nonlinear interpolation. As a byproduct, we prove the equivalence of the two descriptions of quantum Besov spaces, resolving the conjecture proposed in \cite[Remark 3.16]{McNLE}. |
| title | The nonlinear estimates on quantum Besov spaces |
| topic | Functional Analysis Analysis of PDEs 46L52, 42B37, 35Q30 |
| url | https://arxiv.org/abs/2601.11934 |