Parabolic Extrapolation and Its Applications to Characterizing Parabolic BMO Spaces via Parabolic Fractional Commutators
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909551547121664 |
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| author | Cao, Mingming Kong, Weiyi Yang, Dachun Yuan, Wen Zhu, and Chenfeng |
| author_facet | Cao, Mingming Kong, Weiyi Yang, Dachun Yuan, Wen Zhu, and Chenfeng |
| contents | In this article, we establish the parabolic version of the celebrated Rubio de Francia extrapolation theorem. As applications, we obtain new characterizations of parabolic BMO-type spaces in terms of various commutators of parabolic fractional operators with time lag. The key tools to achieve these include to establish the appropriate form in the parabolic setting of the parabolic Rubio de Francia iteration algorithm, the Cauchy integral trick, and a modified Fourier series expansion argument adapted to the parabolic geometry. The novelty of these results lies in the fact that, for the first time, we not only introduce a new class of commutators associated with parabolic fractional integral operators with time lag, but also utilize them to provide a characterization of the parabolic BMO-type space in the high-dimensional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19393 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parabolic Extrapolation and Its Applications to Characterizing Parabolic BMO Spaces via Parabolic Fractional Commutators Cao, Mingming Kong, Weiyi Yang, Dachun Yuan, Wen Zhu, and Chenfeng Functional Analysis Analysis of PDEs Classical Analysis and ODEs Primary 47B47, Secondary 42B25, 42B35, 47A30, 46E35 In this article, we establish the parabolic version of the celebrated Rubio de Francia extrapolation theorem. As applications, we obtain new characterizations of parabolic BMO-type spaces in terms of various commutators of parabolic fractional operators with time lag. The key tools to achieve these include to establish the appropriate form in the parabolic setting of the parabolic Rubio de Francia iteration algorithm, the Cauchy integral trick, and a modified Fourier series expansion argument adapted to the parabolic geometry. The novelty of these results lies in the fact that, for the first time, we not only introduce a new class of commutators associated with parabolic fractional integral operators with time lag, but also utilize them to provide a characterization of the parabolic BMO-type space in the high-dimensional case. |
| title | Parabolic Extrapolation and Its Applications to Characterizing Parabolic BMO Spaces via Parabolic Fractional Commutators |
| topic | Functional Analysis Analysis of PDEs Classical Analysis and ODEs Primary 47B47, Secondary 42B25, 42B35, 47A30, 46E35 |
| url | https://arxiv.org/abs/2503.19393 |