Molecular decomposition of anisotropic homogeneous mixed-norm spaces with applications to the boundedness of operators
Anisotropic homogeneous mixed-norm Besov and Triebel–Lizorkin spaces are introduced and their properties are explored. A discrete adapted φ-transform decomposition is obtained. An associated class of almost diagonal operators is introduced and a boundedness result for such operators is obtained. Mol...
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| Published in | Applied and computational harmonic analysis Vol. 47; no. 2; pp. 447 - 480 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
01.09.2019
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1063-5203 1096-603X |
| DOI | 10.1016/j.acha.2017.10.001 |
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| Abstract | Anisotropic homogeneous mixed-norm Besov and Triebel–Lizorkin spaces are introduced and their properties are explored. A discrete adapted φ-transform decomposition is obtained. An associated class of almost diagonal operators is introduced and a boundedness result for such operators is obtained. Molecular decompositions for all the considered spaces are derived with the help of the algebra of almost diagonal operators. As an application, we obtain boundedness results on the considered spaces for Fourier multipliers and for pseudodifferential operators with suitable adapted homogeneous symbols using the molecular decomposition theory. |
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| AbstractList | Anisotropic homogeneous mixed-norm Besov and Triebel–Lizorkin spaces are introduced and their properties are explored. A discrete adapted φ-transform decomposition is obtained. An associated class of almost diagonal operators is introduced and a boundedness result for such operators is obtained. Molecular decompositions for all the considered spaces are derived with the help of the algebra of almost diagonal operators. As an application, we obtain boundedness results on the considered spaces for Fourier multipliers and for pseudodifferential operators with suitable adapted homogeneous symbols using the molecular decomposition theory. |
| Author | Georgiadis, Athanasios G. Cleanthous, Galatia Nielsen, Morten |
| Author_xml | – sequence: 1 givenname: Galatia surname: Cleanthous fullname: Cleanthous, Galatia email: gkleanth@math.auth.gr organization: Department of Mathematics, Aristotle University of Thessaloniki, Greece – sequence: 2 givenname: Athanasios G. surname: Georgiadis fullname: Georgiadis, Athanasios G. email: nasos@math.aau.dk organization: Department of Mathematical Sciences, Aalborg University, Denmark – sequence: 3 givenname: Morten orcidid: 0000-0002-9078-0594 surname: Nielsen fullname: Nielsen, Morten email: mnielsen@math.aau.dk organization: Department of Mathematical Sciences, Aalborg University, Denmark |
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| Keywords | secondary Fourier multipliers Wavelets Pseudodifferential operators φ-Transform Almost diagonal operators Anisotropic Mixed-norms Besov spaces primary Triebel–Lizorkin spaces |
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| Snippet | Anisotropic homogeneous mixed-norm Besov and Triebel–Lizorkin spaces are introduced and their properties are explored. A discrete adapted φ-transform... |
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| SubjectTerms | Almost diagonal operators Anisotropic Besov spaces Fourier multipliers Mixed-norms Pseudodifferential operators Triebel–Lizorkin spaces Wavelets φ-Transform |
| Title | Molecular decomposition of anisotropic homogeneous mixed-norm spaces with applications to the boundedness of operators |
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