A class of Caffarelli-Kohn-Nirenberg type inequalities on the \(H\)-type group. (English) Zbl 1320.46037
Summary: This work is devoted to establish a class of Caffarelli-Kohn-Nirenberg type inequalities on the \(H\)-type group. Inspired by the idea of J. L. Chern and C. S. Lin, 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.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 22E30 | Analysis on real and complex Lie groups |
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