Interpolation properties of a scale of spaces
The scale \(A_{p,r},\) with \(1\leq p,r\leq \infty,\) is considered. Here \[ \| f\|_{A_{p,r}}=\left (\int_{0}^{\infty}\left (\frac{1}{u}\int_{u\leq | \zeta| \leq 2u}| f(\zeta)| ^{p}d\zeta\right)^{r/p}du \right )^{1/r}, \] where \(1\leq p,r<\infty.\) It is proved that the real interpolation space of two spaces from the above scale does not belong in general to the same scale. The spaces \(A_{p,r}\) are frequently used in analysis.
scientific article; zbMATH DE number 2162762