Stability estimates for $L^p$-Caffarelli-Kohn-Nirenberg inequalities

Based on some new vector inequalities established by Figalli and Zhang [\emph{Duke Math. J.} $\mathbf{\text{171}}$ (2022), 2407–2459], we study the stability of the scale invariant and the scale non-invariant $L^p$-Caffarelli-Kohn-Nirenberg inequalities, which fills the recent work of Do \emph{et al.} [$L^p$-Caffarelli-Kohn-Nirenberg inequalities and their stabilities, arXiv: 2310.07083] for $1<p<2$, and also extends some results of Cazacu \emph{et al.} [\emph{J. Math. Pures Appl. (9)} $\mathbf{\text{182}}$ (2024), 253–284] to a general case for $L^p$-Caffarelli-Kohn-Nirenberg inequalities with $1<p<N$.