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arXiv · 2402.18504

Sawyer estimates of mixed type for operators associated to a critical radius function

Fabio Berra·Gladis Pradolini·Pablo Quijano
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Abstract

We prove mixed inequalities for the Hardy-Littlewood maximal function $M^{\rho,\sigma}$, where $\rho$ is a critical radius function and $\sigma\geq 0$. We also exhibit and prove an extension of Cruz-Uribe, Martell and P\'erez extrapolation result in \cite{CruzUribe-Martell-Perez} to the setting of Muckenhoupt weights associated to a critical radius function $\rho$. This theorem allows us to give mixed inequalities for Schr\"odinger-Calder\'on-Zygmund operators, extending some previous estimates that we have already proved in \cite{BPQ}. Since we are dealing with unrelated weights, the proof involves a quite subtle argument related with the original ideas from Sawyer in \cite{Sawyer}.

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Fabio Berra, Gladis Pradolini, Pablo Quijano. 2024-02-28. Sawyer estimates of mixed type for operators associated to a critical radius function. https://arxiv.org/abs/2402.18504

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