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

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 \(\mathbb{R}^{n_1+n_2}.\)