Weighted inequalities for geometric means
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- by B. Opic and P. Gurka
- Proc. Amer. Math. Soc. 120 (1994), 771-779
- DOI: https://doi.org/10.1090/S0002-9939-1994-1169043-4
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Abstract:
A characterization of weights $u,v$ is given for which the geometric mean operator $Tf(x) = \exp (\tfrac {1} {x}\int _0^x {\ln \;f(t) dt)}$, defined for $f$ positive a.e. on $(0,\infty )$, is bounded from ${L^p}((0,\infty );v dx)$ to ${L^q}((0,\infty );u dx),p \in (0,\infty )$ and $q \in [p,\infty )$.References
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Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 771-779
- MSC: Primary 26D15; Secondary 26D10, 47G10
- DOI: https://doi.org/10.1090/S0002-9939-1994-1169043-4
- MathSciNet review: 1169043