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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator


Author: Eric Sawyer
Journal: Trans. Amer. Math. Soc. 281 (1984), 329-337
MSC: Primary 26D10; Secondary 42B25, 46E30
MathSciNet review: 719673
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Abstract: Characterizations are obtained for those pairs of weight functions $ w,\upsilon $ for which the Hardy operator $ Tf(x) = \int_0^x {f(s)\;ds} $ is bounded from the Lorentz space $ {L^{r,s}}((0,\infty ),\upsilon \,dx)$ to $ {L^{p,q}}((0,\infty ),w\,dx),0 < p,q,r,s \leqslant \infty $. The modified Hardy operators $ {T_\eta }f(x) = {x^{ - \eta }}Tf(x)$ for $ \eta $ real are also treated.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0719673-4
PII: S 0002-9947(1984)0719673-4
Article copyright: © Copyright 1984 American Mathematical Society