Quantitative Weighted Estimates for Schrödinger Pseudo-Multipliers and its Commutators

2025/10/21 by Bagchi, Sayan, Basak, Riju, Singh, Joydwip +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.18219

Abstract

In this article, we investigate the unweighted and weighted L^p-boundedness of pseudo-multipliers associated with a class of Schrödinger operators. 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 Hölder's inequality and quantitative weighted estimates for general sparse operators, which are of independent interest. We also study commutators of Schrödinger pseudo-multipliers, establishing their boundedness and compactness results on these weighted L^p-spaces.

Citations

• L^p-bounds for pseudo-differential operators on graded Lie groups
• Some remarks on the pointwise sparse domination
• Compactness of Riesz transform commutator on stratified Lie groups
• Compactness of Riesz transform commutator associated with Bessel operators
• On pointwise and weighted estimates for commutators of Calderón-Zygmund operators
• Intuitive dyadic calculus: the basics
• On characterization of Poisson integrals of Schrödinger operators with Morrey traces
• On Hermite pseudo-multipliers
• Pseudodifferential operators associated with a semigroup of operators
• Weighted inequalities for commutators of Schrödinger-Riesz transforms
• Weighted norm inequalities for Schrödinger type operators
• Weighted norm inequalities for Schrödinger type operators
• Estimates for translation invariant operators in Lp spaces

Related

• Weighted norm inequalities for pseudo-differential operators and their commutators
• Weighted norm inequalities, spectral multipliers and Littlewood-Paley operators in the Schrödinger settings
• On Hermite pseudo-multipliers
• Weighted norm inequalities for pseudo-differential operators with smooth symbols and their commutators
• Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces