Rendiconti del Seminario Matematico della Università di Padova


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Volume 132, 2014, pp. 249–266
DOI: 10.4171/RSMUP/132-13

Published online: 2014-11-04

A class of Caffarelli–Kohn–Nirenberg type inequalities on the H-type group

Shutao Zhang[1], Yazhou Han[2] and Jingbo Dou[3]

(1) China Jiliang University, Hangzhou, China
(2) China Jiliang University, Hangzhou, China
(3) XI'AN University of Finance and Economics, Xian, Shaanxi, China

This work is devoted to establish a class of Caffarelli-Kohn-Nirenberg type inequalities on the H-type group. Inspired by the idea of Chern J.L. and Lin C.S., a function transformation is introduced. Combining some elementary inequalities and some accurate estimates, we establish a class of weighted Hardy-Sobolev type inequalities and then obtain our main result, namely Caffarelli-Kohn-Nirenberg type inequalities on the H-type group.

Keywords: Caffarelli–Kohn_Nirenberg type inequality, Hardy–Sobolev type inequality, H-type group

Zhang Shutao, Han Yazhou, Dou Jingbo: A class of Caffarelli–Kohn–Nirenberg type inequalities on the H-type group. Rend. Sem. Mat. Univ. Padova 132 (2014), 249-266. doi: 10.4171/RSMUP/132-13