We characterize the pairs of weights ( w , v ) (w,v) for which the modified Hardy operator T f ( x ) = g ( x ) ∫ 0 x f Tf(x)=g(x)∫ ₀ˣf applies L p ( v ) Lᵖ(v) into weak- L q ( w ) Lq(w) where g g is a monotone function and 1 ≤ q > p > ∞ 1≤ q>p>∞ .
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Martín-Reyes et al. (1998) studied this question.
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