Unboundedness properties of smoothness Morrey spaces of regular distributions on domains
type: Item
instance of: scholarly article
title: Unboundedness properties of smoothness Morrey spaces of regular distributions on domains
zbMATH Open document ID: 1393.46025
author: Susana D. Moura
author: Cornelia Schneider
author: Leszek Skrzypczak
author: Dorothee D. Haroske
published in: Science China. Mathematics
publication date: 2018-02-13T00:00:00Z
review text: Let \(X\) be a quasi-Banach space on the domain \(\Omega\) in \(\mathbb R^n\) consisting entirely of regular distributions. Then \[ E^X_G (t) = \sup \big\{ f^* (t): \| f \mid X \| \leq 1 \big\}, \quad t>0, \] is called the growth envelope function. Here, \(f^* (t)\) is the usual rearrangement of \(f \in X\). If \(X\) is not embedded in \(L_\infty (\Omega)\), then the growth envelope function describes the possible unboundedness of the elements of \(X\). The corresponding theory for the well-known spaces \(B^s_{p,q} (\Omega)\) and \(F^s_{p,q} (\Omega)\), which are based on \(L_p\)-spaces, has been developed in detail, mainly by the first-named author. The paper deals with the corresponding theory where the basic Lebesgue spaces \(L_p (\Omega)\) are replaced by the Morrey spaces \(M_{u,p} (\Omega)\), resulting in related smoothness Morrey spaces. It turns out that a substantial theory can only be expected if the domain \(\Omega\) is bounded. Applications to approximation numbers for related compact embeddings are given.
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47B06
zbMATH DE Number: 6837677
zbMATH Keywords: Morrey spaces
zbMATH Keywords: Besov spaces
zbMATH Keywords: Triebel-Lizorkin spaces
zbMATH Keywords: growth envelopes
zbMATH Keywords: atomic decompositions
MaRDI profile type: Publication
full work available at URL: s11425-017-9113-9
OpenAlex ID: W2755278671
Wikidata QID: Q57339723
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DOI: 10.1007/S11425-017-9113-9
description: scientific article; zbMATH DE number 6837677