Multilinear extrapolation of compactness on mixed-norm spaces
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910279166590976 |
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| author | Cao, Mingming Du, Binyu Liu, Honghai Si, Zengyan Yabuta, Kôzô |
| author_facet | Cao, Mingming Du, Binyu Liu, Honghai Si, Zengyan Yabuta, Kôzô |
| contents | In this paper, we develop the Rubio de Francia extrapolation theorem for the multilinear compactness on mixed-norm Lebesgue spaces. More precisely, if a multilinear operator is bounded on weighted product spaces, then its compactness can be extrapolated from unweighted product spaces to the full range of weighted mixed-norm spaces. This result is mainly based on a multilinear interpolation theorem of compactness on weighted mixed-norm spaces, for which we present a characterization of compactness on mixed-norm spaces and a multilinear interpolation theorem of boundedness on multi-mixed-norm spaces. As applications of the extrapolation theorem, we obtain compactness results for several kinds of bi-parameter operators on weighted mixed-norm spaces, including multilinear bi-parameter Calderón-Zygmund operators, multilinear bi-parameter dyadic paraproducts, bilinear bi-parameter continuous paraproducts, and bilinear bi-parameter pseudo-differential operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_01523 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multilinear extrapolation of compactness on mixed-norm spaces Cao, Mingming Du, Binyu Liu, Honghai Si, Zengyan Yabuta, Kôzô Classical Analysis and ODEs 42B20, 42B25, 42B35 In this paper, we develop the Rubio de Francia extrapolation theorem for the multilinear compactness on mixed-norm Lebesgue spaces. More precisely, if a multilinear operator is bounded on weighted product spaces, then its compactness can be extrapolated from unweighted product spaces to the full range of weighted mixed-norm spaces. This result is mainly based on a multilinear interpolation theorem of compactness on weighted mixed-norm spaces, for which we present a characterization of compactness on mixed-norm spaces and a multilinear interpolation theorem of boundedness on multi-mixed-norm spaces. As applications of the extrapolation theorem, we obtain compactness results for several kinds of bi-parameter operators on weighted mixed-norm spaces, including multilinear bi-parameter Calderón-Zygmund operators, multilinear bi-parameter dyadic paraproducts, bilinear bi-parameter continuous paraproducts, and bilinear bi-parameter pseudo-differential operators. |
| title | Multilinear extrapolation of compactness on mixed-norm spaces |
| topic | Classical Analysis and ODEs 42B20, 42B25, 42B35 |
| url | https://arxiv.org/abs/2606.01523 |