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Proceedings of the American Mathematical Society

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

 

 

$ L\sb{p,\,q}$ modulars


Author: Hidegoro Nakano
Journal: Proc. Amer. Math. Soc. 50 (1975), 201-204
MSC: Primary 46B99
DOI: https://doi.org/10.1090/S0002-9939-1975-0370143-5
MathSciNet review: 0370143
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Abstract: For $ 1 < p \leq q$, a convex modular $ m$ on a linear space $ S$ is called an $ {L_{p,q}}$ modular if $ {\operatorname{Min} _{r = p,q}}{\xi ^r}m(x) \leq m(\xi x) \leq {\operatorname{Max} _{r = p,q}}{\xi ^r}m(x)$ for $ \xi > 0$ and $ x \in S$. We generalize the Minkowski inequality and the Hölder inequality for $ {L_{p,q}}$ modulars.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0370143-5
Keywords: Normed linear spaces, Banach spaces
Article copyright: © Copyright 1975 American Mathematical Society