Refined general weighted $L^{p}$-Hardy and Caffarelli-Kohn-Nirenberg type inequalities and identities related to the Baouendi-Grushin operator

Abstract: In this paper, we present refined general weighted $L^{p}$-Hardy type inequalities and identities with explicit remainder terms associated with Baouendi-Grushin vector fields, thereby improving previously known results. Furthermore, we obtain the corresponding general weighted Caffarelli-Kohn-Nirenberg type inequalities with remainder terms, which, as a result, imply Heisenberg-Pauli-Weyl type inequalities.