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arXiv · 2510.18219

On Schr\"odinger Pseudo-Multipliers and their Commutators

Sayan Bagchi·Riju Basak·Joydwip Singh·Manasa N. Vempati
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Abstract

In this article, we establish the unweighted and weighted $L^p$-boundedness of pseudo-multipliers associated with a class of Schr\"odinger operators, this generalizes the result of our first author and Thangavelu [Bagchi \& Thangavelu, J. Funct. Anal. 2015] for Hermite pseudo-multipliers. The weight classes we consider are tailored to this framework and strictly contain the classical Muckenhoupt $A_p$-classes. To establish the weighted boundedness, we prove a quantitative version of reverse H\"older's inequality and quantitative weighted estimates for general sparse operators, which are of independent interest. We also study commutators of Schr\"odinger pseudo-multipliers, establishing their boundedness and compactness results on these weighted $L^p$-spaces.

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Sayan Bagchi, Riju Basak, Joydwip Singh, Manasa N. Vempati. 2025-10-21. On Schr\"odinger Pseudo-Multipliers and their Commutators. https://arxiv.org/abs/2510.18219

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