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arXiv · 2605.08473

Characterization of weights for the variable fractional maximal operator and weighted inequalities for variable fractional rough operators

Rodrigo M. Pastrana·M. Silvina Riveros·Raúl E. Vidal
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Abstract

We characterize the class of weights related to the boundedness of variable fractional maximal operator $M_{\beta(\cdot),r(\cdot)}$ on variable Lebesgue spaces. This extend previously known results, including those corresponding to the fractional operator $M_{\beta(\cdot),1}$. In addition, we introduce a class of kernels $K$ satisfying a new variable H\"ormander-type condition $H_{\beta(\cdot),r(\cdot)}$. For the fractional operator $T_{\beta(\cdot)}$ given by a kernel in $H_{\beta(\cdot),r(\cdot)}$, we prove a Coifman-Fefferman inequality and weighted inequalities in variable Lebesgue space. Finally, we provide examples of kernels in this variable H\"ormander class.

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Rodrigo M. Pastrana, M. Silvina Riveros, Raúl E. Vidal. 2026-05-08. Characterization of weights for the variable fractional maximal operator and weighted inequalities for variable fractional rough operators. https://arxiv.org/abs/2605.08473

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