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Ostrowski type inequalities related to the generalized Baouendi-Grushin vector fields. (English) Zbl 1273.26023
Summary: We employ a new method to prove a representation formula related to the generalized Baouendi-Grushin vector fields, and then the Ostrowski-type inequalities are 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.
MSC:
26D10 Inequalities involving derivatives and differential and integral operators
35J70 Degenerate elliptic equations
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