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arXiv · 2412.19900

Weighted mixed inequalities for commutators of Schr\"odinger type operators

Fabio Berra·Gladis Pradolini·Jorgelina Recchi
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Abstract

We obtain weighted mixed inequalities for the first order commutator of singular integral operators in the Schr\"odinger setting. Concretely, for $0<\delta\leq 1$ we give estimates of commutators of Schr\"odinger-Calder\'on-Zygmund operators of $(s,\delta)$ type with $1<s\leq \infty$, and $\text{BMO}(\rho)$ symbols associated to a critical radious function $\rho$. Our results generalizes some previous estimates about mixed inequalities for Schr\"odinger type operators. We also deal with $A_p^\rho$ weights, which can be understood as a perturbation of the $A_p$ Muckenhoupt classes by means of function $\rho$.

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Fabio Berra, Gladis Pradolini, Jorgelina Recchi. 2024-12-27. Weighted mixed inequalities for commutators of Schr\"odinger type operators. https://arxiv.org/abs/2412.19900

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