Caffarelli-Kohn-Nirenberg-type inequalities related to weighted p-Laplace equations

In this paper, we consider the Caffarelli-Kohn-Nirenberg-type inequality in radial space which admits wider region of parameters than in general space. Firstly, we give the classification of solutions to a linearized problem related to its extremal functions. Then as an application, we investigate the gradient type remainder term of Caffarelli-Kohn-Nirenberg-type inequality by using spectral estimate combined with a compactness argument which extends the work of Figalli and Zhang (2022) [20] at least for radial case.