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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.07781 |
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| _version_ | 1866914950467813376 |
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| author | Lerner, Andrei K. |
| author_facet | Lerner, Andrei K. |
| contents | The classical Muckenhoupt's $A_p$ condition is necessary and sufficient for the boundedness of the maximal operator $M$ on $L^p(w)$ spaces. In this paper we obtain another characterization of the $A_p$ condition. As a result, we show that some strong versions of the weighted $L^p(w)$ Coifman--Fefferman and Fefferman--Stein inequalities hold if and only if $w\in A_p$. We also give new examples of Banach function spaces $X$ such that $M$ is bounded on $X$ but not bounded on the associate space $X'$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a non-standard characterization of the $A_p$ condition Lerner, Andrei K. Classical Analysis and ODEs The classical Muckenhoupt's $A_p$ condition is necessary and sufficient for the boundedness of the maximal operator $M$ on $L^p(w)$ spaces. In this paper we obtain another characterization of the $A_p$ condition. As a result, we show that some strong versions of the weighted $L^p(w)$ Coifman--Fefferman and Fefferman--Stein inequalities hold if and only if $w\in A_p$. We also give new examples of Banach function spaces $X$ such that $M$ is bounded on $X$ but not bounded on the associate space $X'$. |
| title | On a non-standard characterization of the $A_p$ condition |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2409.07781 |