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Weighted norm inequalities for homogeneous families of operators


Author: José L. Rubio de Francia
Journal: Trans. Amer. Math. Soc. 275 (1983), 781-790
MSC: Primary 42B25; Secondary 43A85
DOI: https://doi.org/10.1090/S0002-9947-1983-0682732-8
MathSciNet review: 682732
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Abstract: If a family of operators in $ {R^n}$ is invariant under rotations and dilations and satisfy a certain inequality in $ {L^p}({l^r})$, then it is uniformly bounded in the weighted space $ {L^r}(\vert x\vert{^{n(r/p - 1)}}\,dx)$. This is the main consequence of a more general result for operators in homogeneous spaces. Applications are given to certain maximal operators, the Fourier transform and Bochner-Riesz multipliers.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0682732-8
Keywords: Weighted norm inequalities, rotation and dilation invariant operators, vector valued inequalities, amenable groups
Article copyright: © Copyright 1983 American Mathematical Society

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