Resumen de Integral conditions for Hardy-type operators involving suprema

Martin Krepela

• We characterize the validity of the weighted inequality (∫∞0[sup?∈[?,∞)?(?)∫∞??(?)d?]??(?)d?)1?≤?(∫∞0??(?)?(?)d?)1? for all nonnegative functions g on (0,∞) , with exponents in the range 1≤?<∞ and 0

  Moreover, we give an integral characterization of the inequality (∫∞0[sup?∈[?,∞)?(?)?(?)]??(?)d?)1?≤?(∫∞0??(?)?(?)d?)1? being satisfied for all nonnegative nonincreasing functions f on (0,∞) in the case 0