Abstract
For nonnegative Borel measures μ \mu on R 1 R^1 and for the maximal geometric mean operator G f G_f , we characterize the weight pairs ( w , v ) (w,v) for which G f G_f is of weak type ( p , p ) (p,p) and of strong type ( p , p ) (p,p) , 0 > p > ∞ 0>p>\infty . No doubling conditions are needed. We also note that a previously published different characterization for the strong type inequality for G f G_f has an incorrect proof.
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