Rendiconti del Seminario Matematico della Università di Padova
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Ostrowski Type Inequalities Related to the Generalized Baouendi-Grushin Vector FieldsJingbo Dou and Yazhou Han (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