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Transactions of the American Mathematical Society

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

 

 

Estimates for operators in mixed weighted $ L\sp p$-spaces


Author: Hans P. Heinig
Journal: Trans. Amer. Math. Soc. 287 (1985), 483-493
MSC: Primary 42B10; Secondary 44A10, 46M35, 47B38
DOI: https://doi.org/10.1090/S0002-9947-1985-0768721-5
MathSciNet review: 768721
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Abstract: A weighted Marcinkiewicz interpolation theorem is proved. If $ T$ is simultaneously of weak type $ ({p_i},{q_i})$, $ i = 0,1$; $ 1 \leqslant {p_0} < {p_1} \leqslant \infty $ and $ u$, $ v$ certain weight functions, then $ T$ is bounded from $ L_v^p$ to $ L_u^q$ for $ 0 < q < p$, $ p \geqslant 1$. The result is applied to obtain weighted estimates for the Laplace and Fourier transform, as well as the Riesz potential.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0768721-5
Article copyright: © Copyright 1985 American Mathematical Society