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June 2014 Remarks on a Subspace of Morrey Spaces
Takashi IZUMI, Enji SATO, Kôzô YABUTA
Tokyo J. Math. 37(1): 185-197 (June 2014). DOI: 10.3836/tjm/1406552438

Abstract

Let $p$, $\lambda$ be real numbers such that $1<p<\infty$, and $0<\lambda<1$. Also let $L^{p,\lambda}(\mathbb{T})$ be Morrey spaces on the unit circle $\mathbb{T}$, and $L^{p,\lambda}_0(\mathbb{T})$ the closure of $C(\mathbb{T})$ in $L^{p,\lambda}(\mathbb{T})$. Zorko [7] gave the predual $Z^{q,\lambda}(\mathbb{T})\ (1/p+1/q=1)$ of $L^{p,\lambda}(\mathbb{T})$. In this article, we show a property of $L^{p,\lambda}_0(\mathbb{T})$ and prove in detail that $L_0^{p,\lambda}(\mathbb{T})$ is the predual of $Z^{q,\lambda}(\mathbb{T})$, whose fact is stated in Adams-Xiao [1].

Citation

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Takashi IZUMI. Enji SATO. Kôzô YABUTA. "Remarks on a Subspace of Morrey Spaces." Tokyo J. Math. 37 (1) 185 - 197, June 2014. https://doi.org/10.3836/tjm/1406552438

Information

Published: June 2014
First available in Project Euclid: 28 July 2014

zbMATH: 1304.42059
MathSciNet: MR3264521
Digital Object Identifier: 10.3836/tjm/1406552438

Subjects:
Primary: 42A45
Secondary: 42B30

Rights: Copyright © 2014 Publication Committee for the Tokyo Journal of Mathematics

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Vol.37 • No. 1 • June 2014
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