Geodesic
Hardy–Sobolev inequalities for Sobolev functions in central Herz–Morrey spaces on the unit ball
Yoshihiro Mizuta1 ; Tetsu Shimomura2
1 Hiroshima University, Graduate School of Advanced Science and Engineering, Department of Mathematics
2 Hiroshima University, Graduate School of Humanities and Social Sciences, Department of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1031-1052

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Our aim in this paper is to establish Hardy-Sobolev inequalities for Sobolev functions and generalized Riesz potentials in central Herz-Morrey spaces on the unit ball. As an application, we obtain norm inequalities for Green potentials.  
Keywords: Hardy-Sobolev inequality, central Herz-Morrey spaces, Riesz potentials

Yoshihiro Mizuta 1 ; Tetsu Shimomura 2

1 Hiroshima University, Graduate School of Advanced Science and Engineering, Department of Mathematics
2 Hiroshima University, Graduate School of Humanities and Social Sciences, Department of Mathematics 
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Yoshihiro Mizuta; Tetsu Shimomura. Hardy–Sobolev inequalities for Sobolev functions in central Herz–Morrey spaces on the unit ball. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1031-1052. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a24/