Remarks on a subspace of Morrey spaces
\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.
scientific article; zbMATH DE number 6350029