Hardy and Rellich inequalities for anisotropic \(p\)-sub-Laplacians (Q2175548)

The main purpose of the authors is to obtain subelliptic Hardy- and Rellich-type inequalities for the anisotropic \(p\)-sub-Laplacian on stratified groups. The method is mainly based to derive the subelliptic Picone-type identities on stratified groups. As consequences, Hardy- and Rellich-type inequalities for anisotropic sub-Laplacians are presented. The authors present analogues of Hardy-type inequalities with multiple singularities and many-particle Hard- type inequalities on stratified groups, respectively. These inequalities are obtained in their horizontal form in the spirit of previous papers of the authors. Finally, Hardy-type inequalities with exponential weights are shown.