JournalsrsmupVol. 132pp. 249–266

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

  • Shutao Zhang

    China Jiliang University, Hangzhou, China

  • Yazhou Han

    China Jiliang University, Hangzhou, China

  • Jingbo Dou

    XI'AN University of Finance and Economics, Xian, Shaanxi, China
A class of Caffarelli–Kohn–Nirenberg type inequalities on the H-type group cover
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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