Ostrowski Type Inequalities Related to the Generalized Baouendi-Grushin Vector Fields

Abstract

In this paper, we employ a new method to prove a representation formula related to the generalized Baouendi-Grushin vector fields, and then the Ostrowski type inequalities is established in the ball and bounded domain, respectively, via the representation formula and $L^\infty$ norm of the horizontal gradient. In addition, in the same spirit, we show the Hardy inequalities with boundary term related to the generalized Baouendi-Grushin vector fields.