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

 

Fractional integrals on weighted $ H\sp p$ and $ L\sp p$ spaces


Authors: Jan-Olov Strömberg and Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 287 (1985), 293-321
MSC: Primary 42B30; Secondary 26A33, 47G05
MathSciNet review: 766221
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Abstract: We study the two weight function problem $ \parallel {I_\alpha }f{\parallel _{H_u^q}} \leqslant c\parallel f{\parallel _{H_v^p}},0 < p \leqslant q < \infty $ , for fractional integrals on Hardy spaces. If $ u$ and $ v$ satisfy the doubling condition and $ 0 < p \leqslant 1$, we obtain a necessary and sufficient condition for the norm inequality to hold. If $ 1 < p < \infty $ we obtain a necessary condition and a sufficient condition, and show these are the same under various additional conditions on $ u$ and $ v$. We also consider the corresponding problem for $ L_u^q$ and $ L_v^p$, and obtain a necessary and sufficient condition in some cases.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0766221-X
PII: S 0002-9947(1985)0766221-X
Article copyright: © Copyright 1985 American Mathematical Society