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Proceedings of the American Mathematical Society

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

 

 

Lipschitz spaces and mixed Lebesgue spaces


Author: W. R. Madych
Journal: Proc. Amer. Math. Soc. 85 (1982), 213-218
MSC: Primary 46E30; Secondary 42B99, 46M35, 47A30
DOI: https://doi.org/10.1090/S0002-9939-1982-0652445-1
MathSciNet review: 652445
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Abstract: It is shown that translation invariant linear operators which improve Lipschitz classes behave almost as well as the corresponding fractional Riesz transforms when applied to the mixed Lebesgue spaces. These results partially generalize some of the theorems concerning Riesz transforms and mixed Lebesgue classes due to Adams and Bagby, Lizorkin, and others.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0652445-1
Article copyright: © Copyright 1982 American Mathematical Society