Rendiconti del Seminario Matematico della Università di Padova


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Volume 129, 2013, pp. 225–244
DOI: 10.4171/RSMUP/129-13

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

Jingbo Dou[1] and Yazhou Han[2]

(1) School of Statistics, XI'AN University of Finance and Economics, 710100, Xi'an, Shaanxi, China
(2) Department of Mathematics, China Jiliang University, 310018, Hangzhou, China

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.

Keywords: Generalized Baouendi-Grushin vector fields; representation formula; Ostrowski type inequality; Hardy inequality

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