@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/} }
TY - JOUR AU - Zhang, Shutao AU - Han, Yazhou AU - Dou, Jingbo TI - A class of Caffarelli-Kohn-Nirenberg type inequalities on the H-type group JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2014 SP - 249 EP - 266 VL - 132 PB - Seminario Matematico of the University of Padua UR - http://archive.numdam.org/item/RSMUP_2014__132__249_0/ LA - en ID - RSMUP_2014__132__249_0 ER -
%0 Journal Article %A Zhang, Shutao %A Han, Yazhou %A Dou, Jingbo %T A class of Caffarelli-Kohn-Nirenberg type inequalities on the H-type group %J Rendiconti del Seminario Matematico della Università di Padova %D 2014 %P 249-266 %V 132 %I Seminario Matematico of the University of Padua %U http://archive.numdam.org/item/RSMUP_2014__132__249_0/ %G en %F RSMUP_2014__132__249_0
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] 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] Polar coordinates in Carnot groups, Math. Z. 241 (2002), pp. 697–730. | MR | Zbl
- ,[3] A unified approach to improved Hardy inequalities with best constants, Trans. Amer. Math. Soc., 356(6) (2004), pp. 2169–2196. | MR | Zbl
- - ,[4] First order interpolation inequalities with weights. Compositio Math., 53 (1984), pp. 259–275. | Numdam | MR | Zbl
- - ,[5] 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] On Hardy-Sobolev inequality and its application to certain singular problems, PH.D Thesis, Indian Institute of Science, 2001.
,[7] Minimizers of Caffarelli-Kohn-Nirenberg inequalities with the singularity on the boundary. Arch. Rational Mech. Anal., 197 (2010), pp. 401–432. | MR | Zbl
- ,[8] Hardy spaces on homogeneous groups, Princeton Univ. Press, Princeton 1980. | MR | Zbl
- ,[9] Hardy inequalities and some critical elliptic and parabolic problems, J. Differential equations, 144 (1998), pp. 441–476. | MR | Zbl
- ,[10] 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] 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] Multiple solutions for quasilinear PDE involving the critical Sobolev exponent, Trans. Amer. Math. Soc., 352 (2000), pp. 5703–5743. | MR | Zbl
- ,[13] Sobolev interpolation inequalities with weights, Trans. Amer. Math. Soc., 323 (1991), pp. 263–281. | MR | Zbl
- ,[14] Polar coordinates on H-type groups and applications, Vietnam J. Math., 34(3) (2006), pp. 307–316. | MR | Zbl
- ,[15] Hardy-Sobolev type inequalities on the H-type group, Manuscripta Math., 118 (2005), pp. 235–252. | MR | Zbl
- ,[16] 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] 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] 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] 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] Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities, Proc. Amer. Math. Soc., 132 (2004), pp. 1685–1691. | MR | Zbl
- ,[21] Interpolation inequalities with weights. Comm. in Partial Differential Equations, 11(14) (1986), pp. 1515–1538. | MR | Zbl
,[22] 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] 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] Yamabe equations on Carnot groups, PH.D Thesis, Purdue University, December 2000. | MR
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