A note on quarkonial systems and multilevel partition of unity methods1. Issue 5 (7th January 2013)

• Record Type: Journal Article
• Authors: Dahlke, Stephan; Oswald, Peter; Raasch, Thorsten; Haroske, Dorothee D.; Schmeißer, Hans‐Jürgen
• Is Part Of: Mathematische Nachrichten. Volume 286:Issue 5/6(2013)
• Page Start: 600
• Page End: 613
• Publication Date: 2013-01-07
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201100246
• Languages: English
• ISSNs: 0025-584X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We discuss the connection between the theory of quarkonial decompositions for function spaces developed by Hans Triebel, and the multilevel partition of unity method. The central result is an alternative approach to the stability of quarkonial decompositions in Besov spaces <tex-math notation="LaTeX"><![CDATA[\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$B_{pp}^s({\mathbb {R}}^n)$\end{document}]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg1x6rhvjx" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />, <italic>s</italic> &gt; <italic>n</italic>(1/<italic>p</italic> − 1)₊, which leads to relaxed decay assumptions on the elements of a quarkonial system as the monomial degree grows.</p> </abstract>