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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00398 |
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| _version_ | 1866911744608174080 |
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| author | Zhang, Yuxun Zhou, Jiang |
| author_facet | Zhang, Yuxun Zhou, Jiang |
| contents | In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As applications, we obtain the boundedness of convex-set valued fractional averaging operators and fractional maximal operators, and prove the reverse factorization property of matrix weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00398 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Interpolation on Convex-set Valued Lebesgue Spaces and its Applications Zhang, Yuxun Zhou, Jiang Functional Analysis 26E25, 42B25, 42B35 In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As applications, we obtain the boundedness of convex-set valued fractional averaging operators and fractional maximal operators, and prove the reverse factorization property of matrix weights. |
| title | Interpolation on Convex-set Valued Lebesgue Spaces and its Applications |
| topic | Functional Analysis 26E25, 42B25, 42B35 |
| url | https://arxiv.org/abs/2401.00398 |