On the boundedness of the anisotropic fractional maximal operator from anisotropic complementary Morrey-type spaces to anisotropic Morrey-type spaces

The problem of the boundedness of the anisotropic fractional maximal operator $M_\alpha^d$ from anisotropic complementary Morrey-type spaces to anisotropic Morrey-type spaces is reduced to the problem of boundedness of the dual Hardy operator in weighted $L_p$-spaces on the cone of non-negative non-increasing functions, which allows obtaining sharp sufficient conditions for the boundedness of $M_\alpha^d$.