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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the hyperbolic Riesz means


Author: A. El Kohen
Journal: Proc. Amer. Math. Soc. 89 (1983), 113-116
MSC: Primary 42B15
DOI: https://doi.org/10.1090/S0002-9939-1983-0706521-6
MathSciNet review: 706521
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Abstract: We define the hyperbolic Riesz means in $ {{\mathbf{R}}^2}$ by $ {H_\lambda }f = {({m_\lambda }\hat f)^\upsilon }$ where $ {m_\lambda }({\xi _1},{\xi _2}) = (1 - {({\xi _1}{\xi _2})^2})_ + ^\lambda ,\lambda \geqslant 0$, and show that $ {H_\lambda }$ is bounded on $ {L^p}({{\mathbf{R}}^2})$ for $ \tfrac{4}{3} \leqslant p \leqslant 4$ and $ \lambda > \tfrac{1}{2}$ or $ 1 < p < \infty $ and $ \lambda \geqslant 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0706521-6
Article copyright: © Copyright 1983 American Mathematical Society

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