Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



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
MathSciNet review: 682732
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42B25, 43A85

Retrieve articles in all journals with MSC: 42B25, 43A85

Additional Information

Keywords: Weighted norm inequalities, rotation and dilation invariant operators, vector valued inequalities, amenable groups
Article copyright: © Copyright 1983 American Mathematical Society