On some operator-valued Fourier pseudo-multipliers associated to Grushin operators

Abstract

This is a continuation of our work [BBGG23, BBGG22] where we have initiated the study of sparse domination and quantitative weighted estimates for Grushin pseudo-multipliers. In this article, we further extend this analysis to study analogous estimates for a family of operator-valued Fourier pseudo-multipliers associated to Grushin operators $G=-{\Delta }_{x^{\prime }}-|x^{\prime }{|}^2{\Delta }_{x^{\prime \prime }}$ on ${\mathbb{R}}^{n_1+n_2}.$

This work consists of results extracted from arXiv:2112.06634v1. arXiv admin note: substantial text overlap with arXiv:2112.06634

References in corpus (3)

• On $L^2$-boundedness of pseudo-multipliers associated to the Grushin operator
• An optimal multiplier theorem for Grushin operators in the plane, II
• Sparse bounds for pseudo-multipliers associated to Grushin operators, II

Cited by in corpus (1)

• Riesz transforms associated with the Grushin operator with drift