Remarks on a subspace of Morrey spaces
type: Item
instance of: scholarly article
title: Remarks on a subspace of Morrey spaces
zbMATH Open document ID: 1304.42059
author: Takashi Izumi
author: Enji Sato
author: Kôzô Yabuta
published in: Tokyo Journal of Mathematics
publication date: 2014-09-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tjm/1406552438
review text: \textit{C. T. Zorko} [Proc. Am. Math. Soc. 98, 586--592 (1986; Zbl 0612.43003)] identified the predual \(Z^{q, \lambda}(\mathbb{T})\) of the Morrey spaces \(L^{p,\lambda}(\mathbb{T})\) on the unit circle \(\mathbb{T}\) for \(1<p<\infty, 0<\lambda <1, 1/p+1/q =1\) . The closure \(L_0^{p,\lambda}(\mathbb{T})\) of \(C(\mathbb{T})\) in \(L^{p,\lambda}(\mathbb{T})\) was also studied in this paper. In a recent paper on Morrey spaces, \textit{D. R. Adams} and \textit{J. Xiao} [Ark. Mat. 50, No. 2, 201--230 (2012; Zbl 1254.31009)] stated that the predual of \(Z^{q, \lambda}(\mathbb{T})\) itself is nothing but \(L_0^{p,\lambda}(\mathbb{T})\). The paper under review proves this result in detail.
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42B30
zbMATH DE Number: 6350029
zbMATH Keywords: Morrey spaces
zbMATH Keywords: predual
reviewed by: K. Parthasarathy
MaRDI profile type: Publication
OpenAlex ID: W1981982838
cites work: Morrey spaces in harmonic analysis
cites work: Extensions of Hardy spaces and their use in analysis
cites work: Sufficient conditions for three weight sum inequalities in Lebesgue spaces
cites work: Q5667036
cites work: Q3142876
cites work: Q3756738
cites work: Morrey Space
DOI: 10.3836/TJM/1406552438
description: scientific article; zbMATH DE number 6350029