Sharp Rellich–Sobolev inequalities and weighted Adams inequalities involving Hardy terms for bi-Laplacian

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Motivated by a recent work of Dong, Lam and Lu concerning the sharp weighted Trudinger–Moser and Caffarelli–Kohn–Nirenberg inequalities, we derive a sharp Rellich–Sobolev inequality on Rn with n≥5 and weighted Adams inequalities involving Hardy terms on R4. The procedure is based on a quasi-conformal mapping type transform and decomposition into spherical harmonics since the symmetrization arguments do not work in dealing with these inequalities.