Fractional Caffarelli-Kohn-Nirenberg type inequalities on the Heisenberg group

Abstract: The aim of this work is to establish some cases of the Caffarelli-Kohn-Nirenberg inequalities on the Heisenberg group for the fractional Sobolev spaces. Here we work with the fractional Sobolev spaces as given by Adimurthi and Mallick in [1]. Our inequalities also give an improvement on the range of indices for the Hardy type inequality established in [1].