Multivariate Haar systems in Besov function spaces
Multivariate Haar systems in Besov function spaces
View/Date of Publication
03.2020Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
Show full item record
Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11798
Abstract
We determine all cases for which the d-dimensional Haar wavelet system Hd on the unit cube Id is a conditional or unconditional Schauder basis in the classical isotropic Besov function spaces Bsp,q,1(Id), 0 < p, q < ∞, 0 ≤ s < 1/p, defined in terms of first-order Lp moduli of smoothness. We obtain similar results for the tensor-product Haar system Hd, and characterize the parameter range for which the dual of Bsp,q,1(Id) is trivial for 0 < p < 1.
Subjects
Haar system, Besov spaces, Schauder bases in quasi-Banach spaces, unconditional convergence, piecewise constant approximation
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1070/SM9398Part of Series
INS Preprints ; 2002Peter Oswald: Multivariate Haar systems in Besov function spaces. In: INS Preprints, 2002.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11798
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11798
@unpublished{handle:20.500.11811/11798,
author = {{ }},
title = {Multivariate Haar systems in Besov function spaces},
publisher = {Institut für Numerische Simulation (INS)},
year = 2020,
month = mar,
INS Preprints},
volume = 2002,
note = {We determine all cases for which the d-dimensional Haar wavelet system Hd on the unit cube Id is a conditional or unconditional Schauder basis in the classical isotropic Besov function spaces Bsp,q,1(Id), 0 < p, q < ∞, 0 ≤ s < 1/p, defined in terms of first-order Lp moduli of smoothness. We obtain similar results for the tensor-product Haar system Hd, and characterize the parameter range for which the dual of Bsp,q,1(Id) is trivial for 0 < p < 1.},
url = {https://hdl.handle.net/20.500.11811/11798}
}
author = {{ }},
title = {Multivariate Haar systems in Besov function spaces},
publisher = {Institut für Numerische Simulation (INS)},
year = 2020,
month = mar,
INS Preprints},
volume = 2002,
note = {We determine all cases for which the d-dimensional Haar wavelet system Hd on the unit cube Id is a conditional or unconditional Schauder basis in the classical isotropic Besov function spaces Bsp,q,1(Id), 0 < p, q < ∞, 0 ≤ s < 1/p, defined in terms of first-order Lp moduli of smoothness. We obtain similar results for the tensor-product Haar system Hd, and characterize the parameter range for which the dual of Bsp,q,1(Id) is trivial for 0 < p < 1.},
url = {https://hdl.handle.net/20.500.11811/11798}
}
The following license files are associated with this item:
