A simple proof of reverse Sobolev inequalities on the sphere and Sobolev trace inequalities on the unit ball

Runmin Gong, Qiaohua Yang, Shihong Zhang

Frank et al. (J. Funct. Anal., 2022) stated that there is no relation between the reversed Hardy-Littlewood-Sobolev (HLS) inequalities and reverse Sobolev inequalities. However, we…