Limited-Range Multilinear Off-Diagonal Extrapolation and Weighted Transference Principle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912715999543296 |
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| author | Sauer, Jonas |
| author_facet | Sauer, Jonas |
| contents | Multilinear $L^p$ extrapolation results are established in a limited-range, multilinear, and off-diagonal setting for mixed-norm Lebesgue spaces over $σ$-finite measure spaces. Integrability exponents are allowed in the full range $(0,\infty]$. We detach the exponents for the weight classes completely from the exponents for the initial and target spaces for the extrapolation except for the basic consistency condition. This enables to cover the full range $(0,\infty]$ for all integrability exponents and provides new insights into the dependency of the extrapolated bounds on the weight characteristic. Certain endpoint results are new even for $\mathbb{R}^d$. Additionally, in the setting of compact abelian groups, a weighted transference principle is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02139 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limited-Range Multilinear Off-Diagonal Extrapolation and Weighted Transference Principle Sauer, Jonas Analysis of PDEs Classical Analysis and ODEs Functional Analysis 42B25, 42B35, 43A15 Multilinear $L^p$ extrapolation results are established in a limited-range, multilinear, and off-diagonal setting for mixed-norm Lebesgue spaces over $σ$-finite measure spaces. Integrability exponents are allowed in the full range $(0,\infty]$. We detach the exponents for the weight classes completely from the exponents for the initial and target spaces for the extrapolation except for the basic consistency condition. This enables to cover the full range $(0,\infty]$ for all integrability exponents and provides new insights into the dependency of the extrapolated bounds on the weight characteristic. Certain endpoint results are new even for $\mathbb{R}^d$. Additionally, in the setting of compact abelian groups, a weighted transference principle is established. |
| title | Limited-Range Multilinear Off-Diagonal Extrapolation and Weighted Transference Principle |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis 42B25, 42B35, 43A15 |
| url | https://arxiv.org/abs/2511.02139 |