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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Weighted inequalities for geometric means


Authors: B. Opic and P. Gurka
Journal: Proc. Amer. Math. Soc. 120 (1994), 771-779
MSC: Primary 26D15; Secondary 26D10, 47G10
MathSciNet review: 1169043
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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 )$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1169043-4
Article copyright: © Copyright 1994 American Mathematical Society