New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform
We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces 𝒮0(ℝn) and 𝒮(ℍn+1). We then introduce and study a new class of weighted Hölder-Zygmund spaces, where the weights are regularly varying functions. The analysis of these sp...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/815475 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850160075916705792 |
|---|---|
| author | Stevan Pilipović Dušan Rakić Jasson Vindas |
| author_facet | Stevan Pilipović Dušan Rakić Jasson Vindas |
| author_sort | Stevan Pilipović |
| collection | DOAJ |
| description | We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces 𝒮0(ℝn) and 𝒮(ℍn+1). We then introduce and study a new class of weighted Hölder-Zygmund spaces, where the weights are regularly varying functions. The analysis of these spaces is carried out via the wavelet transform and generalized Littlewood-Paley pairs. |
| format | Article |
| id | doaj-art-b1ff6775ceb2476da33f3d89cc2924d5 |
| institution | OA Journals |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-b1ff6775ceb2476da33f3d89cc2924d52025-08-20T02:23:16ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/815475815475New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet TransformStevan Pilipović0Dušan Rakić1Jasson Vindas2Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, SerbiaFaculty of Technology, University of Novi Sad, Bulevar Cara Lazara 1, 21000 Novi Sad, SerbiaDepartment of Mathematics, Ghent University, Krijgslaan 281 Gebouw S22, 9000 Gent, BelgiumWe provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces 𝒮0(ℝn) and 𝒮(ℍn+1). We then introduce and study a new class of weighted Hölder-Zygmund spaces, where the weights are regularly varying functions. The analysis of these spaces is carried out via the wavelet transform and generalized Littlewood-Paley pairs.http://dx.doi.org/10.1155/2012/815475 |
| spellingShingle | Stevan Pilipović Dušan Rakić Jasson Vindas New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform Journal of Function Spaces and Applications |
| title | New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform |
| title_full | New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform |
| title_fullStr | New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform |
| title_full_unstemmed | New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform |
| title_short | New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform |
| title_sort | new classes of weighted holder zygmund spaces and the wavelet transform |
| url | http://dx.doi.org/10.1155/2012/815475 |
| work_keys_str_mv | AT stevanpilipovic newclassesofweightedholderzygmundspacesandthewavelettransform AT dusanrakic newclassesofweightedholderzygmundspacesandthewavelettransform AT jassonvindas newclassesofweightedholderzygmundspacesandthewavelettransform |