Bourgain-Morrey-Lorentz spaces and operators on them
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| Format: | Preprint |
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2025
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| _version_ | 1866910967515840512 |
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| author | Bai, Tengfei Guo, Pengfei Xu, Jingshi |
| author_facet | Bai, Tengfei Guo, Pengfei Xu, Jingshi |
| contents | We introduce Bourgain-Morrey-Lorentz spaces and give a description of the predual of Bourgain-Morrey-Lorentz spaces via the block spaces. As an application of duality, we obtain the boundedness of Hardy-Littlewood maximal operator, sharp maximal operator, Calderón-Zygmund operator, fractional integral operator, commutator on Bourgain-Morrey-Lorentz spaces. Moreover, we obtain a weak Hardy factorization terms of Calderón-Zygmund operator in Bourgain-Morrey-Lorentz spaces. Using this result, we obtain a characterization of functions in $\BMO$ (the functions of ``bounded mean oscillation'') via the boundedness of commutators generated by them and a homogeneous Calderón-Zygmund operator. In the last, we show that the commutator generated by a function $b$ and a homogeneous Calderón-Zygmund operator is a compact operator on Bourgain-Morrey-Lorentz spaces if and only if $b$ is the limit of compactly supported smooth functions in $\BMO$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_19130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bourgain-Morrey-Lorentz spaces and operators on them Bai, Tengfei Guo, Pengfei Xu, Jingshi Functional Analysis Classical Analysis and ODEs 42B35, 42B20, 46E30, 46A20 We introduce Bourgain-Morrey-Lorentz spaces and give a description of the predual of Bourgain-Morrey-Lorentz spaces via the block spaces. As an application of duality, we obtain the boundedness of Hardy-Littlewood maximal operator, sharp maximal operator, Calderón-Zygmund operator, fractional integral operator, commutator on Bourgain-Morrey-Lorentz spaces. Moreover, we obtain a weak Hardy factorization terms of Calderón-Zygmund operator in Bourgain-Morrey-Lorentz spaces. Using this result, we obtain a characterization of functions in $\BMO$ (the functions of ``bounded mean oscillation'') via the boundedness of commutators generated by them and a homogeneous Calderón-Zygmund operator. In the last, we show that the commutator generated by a function $b$ and a homogeneous Calderón-Zygmund operator is a compact operator on Bourgain-Morrey-Lorentz spaces if and only if $b$ is the limit of compactly supported smooth functions in $\BMO$. |
| title | Bourgain-Morrey-Lorentz spaces and operators on them |
| topic | Functional Analysis Classical Analysis and ODEs 42B35, 42B20, 46E30, 46A20 |
| url | https://arxiv.org/abs/2505.19130 |