Interpolation properties of a scale of spaces
type: Item
instance of: scholarly article
title: Interpolation properties of a scale of spaces
zbMATH Open document ID: 1078.46016
published in: Collectanea Mathematica
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/43066
review text: 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.
reviewed by: Nicolae Popa
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 2162762
zbMATH Keywords: interpolation
zbMATH Keywords: real method
zbMATH Keywords: K-functional
author: Andrei K. Lerner
author: Elijah Liflyand
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2162762