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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Boundedness of maximal functions and singular integrals in weighted $ L\sp{p}$ spaces


Author: José L. Rubio de Francia
Journal: Proc. Amer. Math. Soc. 83 (1981), 673-679
MSC: Primary 42B20; Secondary 42B25
MathSciNet review: 630035
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Abstract: Given a weight $ w(x) > 0$ in $ {{\mathbf{R}}^n}$, necessary and sufficient conditions are found for the boundedness of the Hardy-Littlewood maximal function and singular integral operators from $ {L^p}(w)$ to some other weighted $ {L^p}$ space. The dual question is also considered and partially answered.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0630035-3
PII: S 0002-9939(1981)0630035-3
Keywords: Hardy-Littlewood maximal function, singular integral, weighted norm inequalities
Article copyright: © Copyright 1981 American Mathematical Society