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We use variants of the Hardy-Littlewood maximal and the Cruz-Uribe-Neugebauer minimal operators to give direct characterizations of A 1 and RH ∞ that clarify their near symmetry and yield elementary proofs of various known results, including Cruz-Uribe and Neugebauer's refinement of the Jones factorization theorem.

Near-symmetry in 𝐴_{∞} and refined Jones factorization