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

By Lasse Borup, Morten Nielsen. 2008

47 citations recorded by the source corpus.

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 Hormander type classes of pseudo-differential operators adapted to the anisotropy and boundedness of such operators between corresponding Triebel-Lizorkin type spaces is proved.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1e74f64ad712f25c672b1705356b9a6565aa519f

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In Applied Mathematics

1. Morten Nielsen
2. Lasse Borup
3. Hans G. Feichtinger
4. Massimo Fornasier
5. Karlheinz Gröchenig
6. David L. Donoho
7. Athanasios G. Georgiadis
8. E.J. Candes

In Computational Theory and Mathematics

1. Morten Nielsen
2. Lasse Borup
3. L. Susskind
4. Adam R. Brown
5. Ying Zhao
6. R. Myers

Citations in the corpus

• Frame Decomposition of Decomposition Spaces (2007, background): “In the sequel [4] to the present paper, TriebelLizorkin type spaces associated with general coverings of the frequency space are considered.”