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...

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Main Authors: Stevan Pilipović, Dušan Rakić, Jasson Vindas
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
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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.
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issn 0972-6802
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language English
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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
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AT dusanrakic newclassesofweightedholderzygmundspacesandthewavelettransform
AT jassonvindas newclassesofweightedholderzygmundspacesandthewavelettransform