HARDY INEQUALITIES IN HALF SPACES OF THE HEISENBERG GROUP

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Han, JunQiang (DEPARTMENT OF APPLIED MATHEMATICS NORTHWESTERN POLYTECHNICAL UNIVERSITY) ;
Niu, Pengcheng (DEPARTMENT OF APPLIED MATHEMATICS NORTHWESTERN POLYTECHNICAL UNIVERSITY) ;
Qin, Wenji (COLLEGE OF COMPUTER SCIENCE XI'AN POLYTECHNIC UNIVERSITY)

In this paper we prove some Hardy inequalities in the half space of the Heisenberg group and indicate the sharp constant.

L. D'Ambrosio, Some Hardy inequalities on the Heisenberg group, Differ. Uravn. 40 (2004), no. 4, 509-521, 575
L. D'Ambrosio, Some Hardy inequalities on the Heisenberg group, translation in Differ. Equ. 40 (2004), no. 4, 552-564 https://doi.org/10.1023/B:DIEQ.0000035792.47401.2a
N. Garofalo and E. Lanconelli, Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation, Ann. Inst. Fourier (Grenoble) 40 (1990), no. 2, 313-356 https://doi.org/10.5802/aif.1215
J. A. Goldstein and Q. S. Zhang, On a degenerate heat equation with a singular potential, J. Funct. Anal. 186 (2001), no. 2, 342-359 https://doi.org/10.1006/jfan.2001.3792
Y. Han and P. Niu, Some Hardy type inequalities in the Heisenberg group, JIPAM. J. Inequal. Pure Appl. Math. 4 (2003), no. 5, 1-5
P. Niu, H. Zhang, and Y. Wang, Hardy type and Rellich type inequalities on the Heisenberg group, Proc. Amer. Math. Soc. 129 (2001), no. 12, 3623-3630
J. Tidblom, A Hardy inequality in the half-space, J. Funct. Anal. 221 (2005), no. 2, 482-495 https://doi.org/10.1016/j.jfa.2004.09.014

Some Weighted Hardy-Type Inequalities on Anisotropic Heisenberg Groups vol.2011, pp.1, 2011, https://doi.org/10.1155/2011/924840
Picone’s identity for biharmonic operators on Heisenberg group and its applications vol.23, pp.2, 2016, https://doi.org/10.1007/s00030-016-0376-z