WEIGHTED CAFFARELLI-KOHN-NIRENBERG TYPE INEQUALITY ON THE HEISENBERG GROUP

摘要

This work is devoted to establish a class of Caffarelli-Kohn-Nirenberg type inequalities on the Heisenberg group. Inspired by the idea of Chern and 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 Heisenberg group.