On the intermediate spaces and quasi-linearizability of a pair of spaces of Sobolev-Liouville type
type: Item
instance of: scholarly article
title: On the intermediate spaces and quasi-linearizability of a pair of spaces of Sobolev-Liouville type
zbMATH Open document ID: 0911.46020
DOI: 10.1007/BF02771070
author: A. G. Bagdasaryan
published in: Analysis Mathematica
publication date: 1999-01-24T00:00:00Z
review text: The author considers spaces of Sobolev-Liouville type on \({\mathbb R}^n\) with a norm \[ \| f\| =\| F^{-1}(\nu Ff)\| _{L_p({\mathbb R}^n)} \] denoted by \(H_p(\nu)\). Here \(F\) is the Fourier transform, \(1<p<\infty\), and \(\nu\) is a smooth positive weight function satisfying \(| \xi^\gamma D^\gamma \nu(\xi)| \leq c \nu(\xi)\) for \(| \gamma| \leq 1\) and for some constant \(c>0\). It is proved that the couple \(\{H_p(\nu_0),H_p(\nu_1)\}\) is quasilinearizable. As a consequence a trace type theorem for the spaces \(H_p(\nu)\) is derived.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46B70
zbMATH DE Number: 1244246
zbMATH Keywords: Sobolev-Liouville spaces
zbMATH Keywords: interpolation
zbMATH Keywords: trace theorems
zbMATH Keywords: Fourier transform
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1244246