A class of Caffarelli–Kohn–Nirenberg type inequalities on the H-type group
Shutao Zhang
China Jiliang University, Hangzhou, ChinaYazhou Han
China Jiliang University, Hangzhou, ChinaJingbo Dou
XI'AN University of Finance and Economics, Xian, Shaanxi, China
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Abstract
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.
Cite this article
Shutao Zhang, Yazhou Han, Jingbo Dou, A class of Caffarelli–Kohn–Nirenberg type inequalities on the H-type group. Rend. Sem. Mat. Univ. Padova 132 (2014), pp. 249–266
DOI 10.4171/RSMUP/132-13