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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
References
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • 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