Rendiconti del Seminario Matematico della Università di Padova


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

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

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

(1) Department of Mathematics, China Jiliang University, 310018, Hangzhou, China
(2) Department of Mathematics, China Jiliang University, 310018, Hangzhou, China
(3) School of Statistics, XI'AN University of Finance and Economics, 710100, Xi'an, 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