$L_{p, q}$ modulars
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- by Hidegoro Nakano PDF
- Proc. Amer. Math. Soc. 50 (1975), 201-204 Request permission
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.References
- Hidegorô Nakano, Topology of linear topological spaces, Maruzen Co. Ltd., Tokyo, 1951. MR 0046560
- Hidegoro Nakano, Generalized modular spaces, Studia Math. 31 (1968), 439–449. MR 234248, DOI 10.4064/sm-31-5-439-449 —, ${L_p}$ modulars (to appear).
Additional Information
- © Copyright 1975 American Mathematical Society
- 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