Spaces of Sobolev type with positive smoothness on \(\mathbb R^n\), embeddings and growth envelopes
type: Item
instance of: scholarly article
title: Spaces of Sobolev type with positive smoothness on \(\mathbb R^n\), embeddings and growth envelopes
zbMATH Open document ID: 1202.46040
DOI: 10.1155/2009/815676
author: Cornelia Schneider
published in: Journal of Function Spaces and Applications
publication date: 2010-05-06T00:00:00Z
review text: The author investigates three partly different approaches to Triebel-Lizorkin spaces on \(\mathbb R\). The first approach is the Fourier-analytic one, the second is by differences, and the third by subatomic decompositions. As it has been known before, these approaches coincide for a wide range of the parameters \(s,p\) and \(q\). However, if either \(0< p<1\) or \(0 < q < 1\) and \(s>0\) is small, then they do not. But also in those situations they show the same embedding behaviour into Lorentz spaces, so they differ not much. To a certain extent, this is a surprise. The author also discusses Jawerth-Franke type embeddings and growth envelopes for all three scales.
reviewed by: Winfried Sickel
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 5704729
zbMATH Keywords: Triebel-Lizorkin spaces
zbMATH Keywords: Littlewood-Paley decompositions
zbMATH Keywords: differences
zbMATH Keywords: subatomic decompositions
zbMATH Keywords: diagonal embeddings
zbMATH Keywords: embeddings into Lorentz spaces
zbMATH Keywords: growth envelopes
zbMATH Keywords: Hardy-type inequalities
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2009/815676
OpenAlex ID: W2139581143
description: scientific article; zbMATH DE number 5704729