Ostrowski type inequalities related to the generalized Baouendi-Grushin vector fields
Rendiconti del Seminario Matematico della Università di Padova, Volume 129  (2013), p. 225-244
@article{RSMUP_2013__129__225_0,
     author = {Dou, Jingbo and Han, Yazhou},
     title = {Ostrowski type inequalities related to the generalized Baouendi-Grushin vector fields},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {129},
     year = {2013},
     pages = {225-244},
     zbl = {1273.26023},
     mrnumber = {3090639},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2013__129__225_0}
}
Dou, Jingbo; Han, Yazhou. Ostrowski type inequalities related to the generalized Baouendi-Grushin vector fields. Rendiconti del Seminario Matematico della Università di Padova, Volume 129 (2013) , pp. 225-244. http://www.numdam.org/item/RSMUP_2013__129__225_0/

[1] Adimurthi, Hardy-SobolevAdimurthi 4 (2002), pp. 409-434. | MR 1918752

[2] Adimurthi - M. Esteban 12 (2005), pp. 243-263. | MR 2184082

[3] G. A. Anastassiou, Quantitative Approximations, Chapman and Hall/CRC, Boca Raton/New York, 2001. | MR 1791688

[4] G. A. Anastassiou - J. A. Goldstein, Ostrowski type inequalities over Euclidean domains. Rend. Linc. Matem. Appl., 18 (2007), pp. 305-310. | MR 2318823

[5] G. A. Anastassiou - J. A. Goldstein, Higher order Ostrowski type inequalities over Euclidean domains, J. Math. Anal. Appl., 337 (2008), pp. 962-968. | MR 2386345

[6] L. Caffarelli - L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Part. Diff. Eqs., 32 (2007), pp. 1245-1260. | MR 2354493

[7] W. Cohn - G. Lu, Best constants for Moser-Trudinger inequalities on the Heisenberg group, India. Univ. Math. J., 50 (2001), pp. 1567-1591. | MR 1889071

[8] L. D'Ambrosio, Hardy inequalities related to Grushin type operators, Proc. Amer. Math. Soc., 132 (2004), pp. 725-734. | MR 2019949

[9] L. D'Ambrosio, Hardy type inequalities related to second order degenerate differential operators, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2005), pp. 451-486. | Numdam | MR 2185865

[10] L. D'Ambrosio - S. Lucente, Nonlinear Liouville theorems for Grushin and Tricomi operators, J. Diff. Eqs., 193 (2003), pp. 511-541. | MR 1998967

[11] J. Dou - G. Guo - P. Niu, Hardy inequalities with remainder terms for the generalized Baouendi-Grushin vector fields, Math. Ineq. Appl., 13 (2010), pp. 555-570. | MR 2662838

[12] Y. Dong - G. Lu - L. Sun, Global Poincaré Inequalities on the Heisenberg Group and Applications, Acta Mathematica Sinica, English Series., 23 (2007), pp. 735-744. | MR 2308108

[13] B. Franchi - E. Lanconelli, Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 10 (1983), pp. 523-541. | Numdam | MR 753153

[14] G. B. Folland - E. M. Stein, Hardy spaces on homogeneous groups, Princeton University Press, Princeton, NJ, 1982. | MR 657581

[15] B. Franchi - E. Lanconelli, An embedding theorem for Sobolev spaces related to non-smooth vector fields and Harnack inequality, Comm. Part. Diff. Eqs., 9 (1984), pp. 1237-1264. | MR 764663

[16] B. Lian - Q. Yang, Ostrowski type inequalities on H-type groups, J. Math. Anal. Appl., 365 (2010), pp. 158-166. | MR 2585086

[17] Z. Liu, Some Ostrowski type inequalities, Math. Comp. Model., 48 (2008), pp. 949-960. | MR 2451127

[18] H. Liu - J. Luan, Ostrowski type inequalities in the Grushin plane, J. Ineq. Appl. 2010, Article ID 987484, pp. 1-9. | MR 2607941

[19] P. Niu - J. Dou - H. Zhang, Nonexistence of weak solutions for the p-degenerate subelliptic inequalities constructed by the generalized Baouendi-Grushin vector fields, Georgian Math. J., 12 (2005), pp. 723-738. | MR 2197194

[20] P. Niu - Y. Ou - J. Han, Several Hardy type inequalities with weights related to generalized greiner operator, Canad. Math. Bull., 53 (2010), pp. 153-162. | MR 2583221

[21] A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert. Comment. Math. Helv., 10 (1938), pp. 226-227. | MR 1509574

[22] M. Wang - X. Zhao, Ostrowski type inequalities for higher-order derivatives, J. Ineq. Appl. 2009, Article ID 162689, pp. 1-8. | MR 2534573

[23] M. Zhu - Z. Wang, Hardy inequalities with boundary terms, Electron. J. Diff. Eqs., No. 43 (2003), 8 pp. | MR 1971109