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Two weighted inequalities for convolution maximal operators

Two weighted inequalities for convolution maximal operators

Let ϕ : R → [0, ∞) an integrable function such that ϕχ (-∞,0) = 0 and ϕ is decreasing in (0, ∞).In this paper we characterize the pair of weights (u, v) such that the operators Mτ h ϕf (x) = sup R>0 |f | * [τ h ϕ] …