On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators

On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators

A construction of Triebel-Lizorkin type spaces associated with flexible decompositions of the frequency space ℝd is considered. The class of admissible frequency decompositions is generated by a one parameter group of (anisotropic) dilations on ℝd and a suitable decomposition function. The decomposi...

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Main Authors: Lasse Borup, Morten Nielsen
Format: Article
Language:English
Published: Hindawi Limited 2008-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2008/510584
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spelling doaj-6a487b66630d46c791f01d6e38008f592020-11-24T21:35:41ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022008-01-016210715410.1155/2008/510584On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operatorsLasse Borup0Morten Nielsen1Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg East, DenmarkDepartment of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg East, DenmarkA construction of Triebel-Lizorkin type spaces associated with flexible decompositions of the frequency space ℝd is considered. The class of admissible frequency decompositions is generated by a one parameter group of (anisotropic) dilations on ℝd and a suitable decomposition function. The decomposition function governs the structure of the decomposition of the frequency space, and for a very particular choice of decomposition function the spaces are reduced to classical (anisotropic) Triebel-Lizorkin spaces. An explicit atomic decomposition of the Triebel-Lizorkin type spaces is provided, and their interpolation properties are studied. As the main application, we consider Hörmander type classes of pseudo-differential operators adapted to the anisotropy and boundedness of such operators between corresponding Triebel-Lizorkin type spaces is proved.http://dx.doi.org/10.1155/2008/510584
collection DOAJ
language English
format Article
sources DOAJ
author Lasse Borup
Morten Nielsen
spellingShingle Lasse Borup
Morten Nielsen
On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators
Journal of Function Spaces and Applications
author_facet Lasse Borup
Morten Nielsen
author_sort Lasse Borup
title On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators
title_short On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators
title_full On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators
title_fullStr On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators
title_full_unstemmed On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators
title_sort on anisotropic triebel-lizorkin type spaces, with applications to the study of pseudo-differential operators
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
publishDate 2008-01-01
description A construction of Triebel-Lizorkin type spaces associated with flexible decompositions of the frequency space ℝd is considered. The class of admissible frequency decompositions is generated by a one parameter group of (anisotropic) dilations on ℝd and a suitable decomposition function. The decomposition function governs the structure of the decomposition of the frequency space, and for a very particular choice of decomposition function the spaces are reduced to classical (anisotropic) Triebel-Lizorkin spaces. An explicit atomic decomposition of the Triebel-Lizorkin type spaces is provided, and their interpolation properties are studied. As the main application, we consider Hörmander type classes of pseudo-differential operators adapted to the anisotropy and boundedness of such operators between corresponding Triebel-Lizorkin type spaces is proved.
url http://dx.doi.org/10.1155/2008/510584
work_keys_str_mv AT lasseborup onanisotropictriebellizorkintypespaceswithapplicationstothestudyofpseudodifferentialoperators
AT mortennielsen onanisotropictriebellizorkintypespaceswithapplicationstothestudyofpseudodifferentialoperators
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