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 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.
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Jingbo Dou, Yazhou Han, Ostrowski Type Inequalities Related to the Generalized Baouendi-Grushin Vector Fields. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 225–244DOI 10.4171/RSMUP/129-13