A Sawyer Duality Principle for Radially Monotone Functions in R

Let f be a non-negative function on R, which is radially monotone (0 < f ↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup f↓r ∫ Rn fg (∫ Rn f pv ) 1 p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given.