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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Weighted and vector-valued inequalities for potential operators

Authors: Francisco J. Ruiz Blasco and José L. Torrea Hernández
Journal: Trans. Amer. Math. Soc. 295 (1986), 213-232
MSC: Primary 42B20; Secondary 42B25
MathSciNet review: 831197
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Abstract: In this paper we develop some aspect of a general theory parallel to the Calderón-Zygmund theory for operator valued kernels, where the operators considered map functions defined on $ {R^n}$ into functions defined on $ R_ + ^{n + 1} = {R^n} \times [0,\infty )$.

In particular, we apply the obtained results to get vector-valued inequalities for the Poisson integral and fractional integrals. Some weighted norm inequalities are also considered for fractional integrals.

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Keywords: Poisson integral, Carleson measures, fractional integral, vector-valued inequalities, weighted norm inequalities
Article copyright: © Copyright 1986 American Mathematical Society

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