The reverse Hölder inequality for $\mathcal{A}_{p(\cdot)}$ weights with applications to matrix weights
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911150730379264 |
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| author | Cruz-Uribe, David Penrod, Michael |
| author_facet | Cruz-Uribe, David Penrod, Michael |
| contents | In this paper we prove a reverse Hölder inequality for the variable exponent Muckenhoupt weights $\mathcal{A}_{p(\cdot)}$, introduced by the first author, Fiorenza, and Neugeabauer. All of our estimates are quantitative, showing the dependence of the exponent function on the $\mathcal{A}_{p(\cdot)}$ characteristic. As an application, we use the reverse Hölder inequality to prove that the matrix $\mathcal{A}_{p(\cdot)}$ weights, introduced in our previous paper, have both a right and left-openness property. This result is new even in the scalar case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_12849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The reverse Hölder inequality for $\mathcal{A}_{p(\cdot)}$ weights with applications to matrix weights Cruz-Uribe, David Penrod, Michael Classical Analysis and ODEs 42B25, 42B35 In this paper we prove a reverse Hölder inequality for the variable exponent Muckenhoupt weights $\mathcal{A}_{p(\cdot)}$, introduced by the first author, Fiorenza, and Neugeabauer. All of our estimates are quantitative, showing the dependence of the exponent function on the $\mathcal{A}_{p(\cdot)}$ characteristic. As an application, we use the reverse Hölder inequality to prove that the matrix $\mathcal{A}_{p(\cdot)}$ weights, introduced in our previous paper, have both a right and left-openness property. This result is new even in the scalar case. |
| title | The reverse Hölder inequality for $\mathcal{A}_{p(\cdot)}$ weights with applications to matrix weights |
| topic | Classical Analysis and ODEs 42B25, 42B35 |
| url | https://arxiv.org/abs/2411.12849 |