Mixed-mean inequalities for integral power means over centered and uncentered spheres are proved. Therefrom we deduce the Hardy type inequalities for corresponding averaging operators. Moreover, we discuss estimates related to the spherical maximal functions.
"Mixed means for centered and uncentered averaging operators over spheres and related results." Banach J. Math. Anal. 2 (2) 150 - 162, 2008. https://doi.org/10.15352/bjma/1240336301