Weighted norm inequalities for homogeneous families of operators

Rubio de Francia, José L.

doi:10.1090/S0002-9947-1983-0682732-8

Weighted norm inequalities for homogeneous families of operators
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by José L. Rubio de Francia PDF

Trans. Amer. Math. Soc. 275 (1983), 781-790 Request permission

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 ${L^r}(|x|{^{n(r/p - 1)}} dx)$. 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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