Weighted inequalities for the maximal geometric mean operator

Yin, Xiangrong; Muckenhoupt, Benjamin

doi:10.1090/S0002-9939-96-03252-2

Weighted inequalities for the maximal geometric mean operator
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by Xiangrong Yin and Benjamin Muckenhoupt

Proc. Amer. Math. Soc. 124 (1996), 75-81

DOI: https://doi.org/10.1090/S0002-9939-96-03252-2

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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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