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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weighted inequalities
for the maximal geometric mean operator


Authors: Xiangrong Yin and Benjamin Muckenhoupt
Journal: Proc. Amer. Math. Soc. 124 (1996), 75-81
MSC (1991): Primary 26D15, 42B25
MathSciNet review: 1307575
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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 $G_f$ 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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Additional Information

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

Benjamin Muckenhoupt
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03252-2
PII: S 0002-9939(96)03252-2
Received by editor(s): January 26, 1993
Received by editor(s) in revised form: January 31, 1994, and May 18, 1994
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society