Proceedings of the American Mathematical Society

Author(s): Xiangrong Yin; Benjamin Muckenhoupt
Journal: Proc. Amer. Math. Soc. 124 (1996), 75-81.
MSC (1991): Primary 26D15, 42B25
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Abstract: For nonnegative Borel measures $\mu$ on $R^1$

and for the maximal geometric mean operator $G_f$

, we characterize the weight pairs $(w,v)$

for which

is of weak type $(p,p)$

and of strong type $(p,p)$

, $0<p<\infty$ . No doubling conditions are needed. We also note that a previously published different characterization for the strong type inequality for $G_f$

has an incorrect proof.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 26D15, 42B25

Xiangrong Yin
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

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