A class of Caffarelli-Kohn-Nirenberg type inequalities on the H-type group
Rendiconti del Seminario Matematico della Università di Padova, Volume 132 (2014), pp. 249-266.
@article{RSMUP_2014__132__249_0,
     author = {Zhang, Shutao and Han, Yazhou and Dou, Jingbo},
     title = {A class of {Caffarelli-Kohn-Nirenberg} type inequalities on the {H-type} group},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {249--266},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {132},
     year = {2014},
     mrnumber = {3276834},
     zbl = {06379724},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_2014__132__249_0/}
}
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Zhang, Shutao; Han, Yazhou; Dou, Jingbo. A class of Caffarelli-Kohn-Nirenberg type inequalities on the H-type group. Rendiconti del Seminario Matematico della Università di Padova, Volume 132 (2014), pp. 249-266. http://archive.numdam.org/item/RSMUP_2014__132__249_0/

[1] M. Badiale - G. Tarantello, A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics, Arch. Rational Mech. Anal., 163 (2002), pp. 259–293. | MR | Zbl

[2] Z.M. Balogh - J.T. Tyson, Polar coordinates in Carnot groups, Math. Z. 241 (2002), pp. 697–730. | MR | Zbl

[3] G. Barbatis - S. Filippas - A. Tertikas, A unified approach to improved L p Hardy inequalities with best constants, Trans. Amer. Math. Soc., 356(6) (2004), pp. 2169–2196. | MR | Zbl

[4] L. Caffarelli - R. Kohn - L. Nirenberg, First order interpolation inequalities with weights. Compositio Math., 53 (1984), pp. 259–275. | Numdam | MR | Zbl

[5] F. Catrina - Z.Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions, Comm. Pure and Applied Math., 54 (2001), pp. 229258. | MR | Zbl

[6] N. Chaudhuri, On Hardy-Sobolev inequality and its application to certain singular problems, PH.D Thesis, Indian Institute of Science, 2001.

[7] J.L. Chern - C.S. Lin, Minimizers of Caffarelli-Kohn-Nirenberg inequalities with the singularity on the boundary. Arch. Rational Mech. Anal., 197 (2010), pp. 401–432. | MR | Zbl

[8] G.B. Folland - E.M. Stein, Hardy spaces on homogeneous groups, Princeton Univ. Press, Princeton 1980. | MR | Zbl

[9] J.P. García Azorero - I. Peral Alonso, Hardy inequalities and some critical elliptic and parabolic problems, J. Differential equations, 144 (1998), pp. 441–476. | MR | Zbl

[10] N. Garofalo - D. Vassilev, Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups, Math. Ann., 318 (2000), pp. 453–516. | MR | Zbl

[11] N. Garofalo - D. Vassilev, Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type, Duke Math. J., 106(3) (2001), pp. 411–448. | MR | Zbl

[12] N. Ghoussoub - C. Yuan, Multiple solutions for quasilinear PDE involving the critical Sobolev exponent, Trans. Amer. Math. Soc., 352 (2000), pp. 5703–5743. | MR | Zbl

[13] C.E. Gutierrez - R.L. Wheeden, Sobolev interpolation inequalities with weights, Trans. Amer. Math. Soc., 323 (1991), pp. 263–281. | MR | Zbl

[14] J.Q. Han - P.C. Niu, Polar coordinates on H-type groups and applications, Vietnam J. Math., 34(3) (2006), pp. 307–316. | MR | Zbl

[15] Y.Z. Han - P.C. Niu, Hardy-Sobolev type inequalities on the H-type group, Manuscripta Math., 118 (2005), pp. 235–252. | MR | Zbl

[16] Y.Z. Han - P.C. Niu - S.T. Zhang, On first order interpolation inequalities with weights on the Heisenberg group, Acta Math. Sinica (Engl. Ser.), 27(12) (2011), pp. 2493–2506. | MR | Zbl

[17] Y.Z. Han - S.T. Zhang - J.B. Dou, On first order interpolation inequalities with weights on the H-type group, Bull. Braz. Math. Soc., (N. S.) 42(2) (2011), pp. 185202. | MR | Zbl

[18] A. Kaplan, Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms, Trans. Amer. Math. Soc., 258 (1980), pp. 147153. | MR | Zbl

[19] T. Kusano - J. Jaroš - N. Yoshida, A Picone-type identity and Sturmian comparison and oscillation theorem for a class of half-linear partial differential equations of second order, Nonlinear Anal., 40 (2000), pp. 381395. | MR | Zbl

[20] C. Lin - Z.Q. Wang, Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities, Proc. Amer. Math. Soc., 132 (2004), pp. 1685–1691. | MR | Zbl

[21] C.S. Lin, Interpolation inequalities with weights. Comm. in Partial Differential Equations, 11(14) (1986), pp. 1515–1538. | MR | Zbl

[22] G.Z. Lu, Local and global interpolation inequalities on the Folland-Stein Sobolev spaces and polynomials on stratified groups, Math. Res. Lett., 4(6) (1997), pp. 777–790. | MR | Zbl

[23] G.Z. Lu, Polynomials, higher order Sobolev extension theorems and interpolation inequalities on weighted Folland-Stein spaces on stratified groups, Acta Math. Sinica (Engl. Ser.), 16(3) (2000), pp. 405–444. | MR | Zbl

[24] D.N. Vassilev, Yamabe equations on Carnot groups, PH.D Thesis, Purdue University, December 2000. | MR