Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator
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- by Eric Sawyer PDF
- Trans. Amer. Math. Soc. 281 (1984), 329-337 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 281 (1984), 329-337
- MSC: Primary 26D10; Secondary 42B25, 46E30
- DOI: https://doi.org/10.1090/S0002-9947-1984-0719673-4
- MathSciNet review: 719673