Marcinkiewicz-Zygmund inequalities in variable Lebesgue spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916430022180864 |
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| author | Bonich, Marcos Carando, Daniel Mazzitelli, Martín |
| author_facet | Bonich, Marcos Carando, Daniel Mazzitelli, Martín |
| contents | We study $\ell^r$-valued extensions of linear operators defined on Lebesgue spaces with variable exponent. Under some natural (and usual) conditions on the exponents, we characterize $1\leq r\leq \infty$ such that every bounded linear operator $T\colon L^{q(\cdot)}(Ω_2, μ)\to L^{p(\cdot)}(Ω_1, ν)$ has a bounded $\ell^r$-valued extension. We consider both non-atomic measures and measures with atoms and show the differences that can arise. We present some applications of our results to weighted norm inequalities of linear operators and vector-valued extensions of fractional operators with rough kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16323 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Marcinkiewicz-Zygmund inequalities in variable Lebesgue spaces Bonich, Marcos Carando, Daniel Mazzitelli, Martín Functional Analysis Classical Analysis and ODEs We study $\ell^r$-valued extensions of linear operators defined on Lebesgue spaces with variable exponent. Under some natural (and usual) conditions on the exponents, we characterize $1\leq r\leq \infty$ such that every bounded linear operator $T\colon L^{q(\cdot)}(Ω_2, μ)\to L^{p(\cdot)}(Ω_1, ν)$ has a bounded $\ell^r$-valued extension. We consider both non-atomic measures and measures with atoms and show the differences that can arise. We present some applications of our results to weighted norm inequalities of linear operators and vector-valued extensions of fractional operators with rough kernel. |
| title | Marcinkiewicz-Zygmund inequalities in variable Lebesgue spaces |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2307.16323 |