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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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/510584 |
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| _version_ | 1832551811397976064 |
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| author | Lasse Borup Morten Nielsen |
| author_facet | Lasse Borup Morten Nielsen |
| author_sort | Lasse Borup |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-6a487b66630d46c791f01d6e38008f59 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-6a487b66630d46c791f01d6e38008f592025-02-03T06:00:32ZengWileyJournal 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2008/510584 |
| work_keys_str_mv | AT lasseborup onanisotropictriebellizorkintypespaceswithapplicationstothestudyofpseudodifferentialoperators AT mortennielsen onanisotropictriebellizorkintypespaceswithapplicationstothestudyofpseudodifferentialoperators |