Weighted boundedness for the maximal operator associated with matrices
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912937517514752 |
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| author | Ibañez-Firnkorn, Gonzalo |
| author_facet | Ibañez-Firnkorn, Gonzalo |
| contents | In this paper we study the boundedness on $L^p(w)$ of the maximal operator $M_{A^{-1}}$, defined by $M_{A^{-1}}f(x)=Mf(A^{-1}x)$, that is, the maximal of Hardy-Littlewood composed with a invertible matrix $A$. We present two different results of boundedness and provide a characterization for a particular case of matrices. The main novelty lies in examples illustrating the difference between the class of weights with a matrix, $\mathcal{A}_{A,p}$, and the classical Muckenhoupt weight class, $\mathcal{A}_{p}$.
Finally, we extend these results to the fractional framework, considering the fractional maximal operator $M_{α, A^{-1}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_02126 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted boundedness for the maximal operator associated with matrices Ibañez-Firnkorn, Gonzalo Classical Analysis and ODEs 42B25 In this paper we study the boundedness on $L^p(w)$ of the maximal operator $M_{A^{-1}}$, defined by $M_{A^{-1}}f(x)=Mf(A^{-1}x)$, that is, the maximal of Hardy-Littlewood composed with a invertible matrix $A$. We present two different results of boundedness and provide a characterization for a particular case of matrices. The main novelty lies in examples illustrating the difference between the class of weights with a matrix, $\mathcal{A}_{A,p}$, and the classical Muckenhoupt weight class, $\mathcal{A}_{p}$. Finally, we extend these results to the fractional framework, considering the fractional maximal operator $M_{α, A^{-1}}$. |
| title | Weighted boundedness for the maximal operator associated with matrices |
| topic | Classical Analysis and ODEs 42B25 |
| url | https://arxiv.org/abs/2603.02126 |