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arXiv · 2603.02126

Weighted boundedness for the maximal operator associated with matrices

Gonzalo Ibañez-Firnkorn
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Abstract

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 $M_{\alpha, A^{-1}}$.

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Gonzalo Ibañez-Firnkorn. 2026-03-02. Weighted boundedness for the maximal operator associated with matrices. https://arxiv.org/abs/2603.02126

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