Haar system as Schauder basis in Besov spaces: the limiting cases for 0 < p ≤ 1
Haar system as Schauder basis in Besov spaces: the limiting cases for 0 < p ≤ 1
Dokument öffnen (425KB)Datum der Veröffentlichung
09.2018Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11812
Inhalt
We show that the d-dimensional Haar system Hd on the unit cube Id is a Schauder basis in the classical Besov space Bsp,q,1(Id), 0 < p < 1, defined by first order differences in the limiting case s = d(1/p − 1), if and only if 0 < q ≤ p. For d = 1 and p < q < ∞, this settles the only open case in our 1979 paper [4], where the Schauder basis property of H in Bsp,q,1(I) for 0 < p < 1 was left undecided. We also consider the Schauder basis property of Hd for the standard Besov spaces Bsp,q(Id) defined by Fourier-analytic methods in the limiting cases s = d(1/p−1) and s = 1, complementing results by Triebel [7].
Schlagwörter
Haar system, Besov spaces, Schauder bases in quasi-Banach spaces, spline approximation
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.48550/arXiv.1808.08156Reihe, Nummer
INS Preprints ; 1810Peter Oswald: Haar system as Schauder basis in Besov spaces: the limiting cases for 0 < p ≤ 1. In: INS Preprints, 1810.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11812
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11812
@unpublished{handle:20.500.11811/11812,
author = {{ }},
title = {Haar system as Schauder basis in Besov spaces: the limiting cases for 0 < p ≤ 1},
publisher = {Institut für Numerische Simulation (INS)},
year = 2018,
month = sep,
INS Preprints},
volume = 1810,
note = {We show that the d-dimensional Haar system Hd on the unit cube Id is a Schauder basis in the classical Besov space Bsp,q,1(Id), 0 < p < 1, defined by first order differences in the limiting case s = d(1/p − 1), if and only if 0 < q ≤ p. For d = 1 and p < q < ∞, this settles the only open case in our 1979 paper [4], where the Schauder basis property of H in Bsp,q,1(I) for 0 < p < 1 was left undecided. We also consider the Schauder basis property of Hd for the standard Besov spaces Bsp,q(Id) defined by Fourier-analytic methods in the limiting cases s = d(1/p−1) and s = 1, complementing results by Triebel [7].},
url = {https://hdl.handle.net/20.500.11811/11812}
}
author = {{ }},
title = {Haar system as Schauder basis in Besov spaces: the limiting cases for 0 < p ≤ 1},
publisher = {Institut für Numerische Simulation (INS)},
year = 2018,
month = sep,
INS Preprints},
volume = 1810,
note = {We show that the d-dimensional Haar system Hd on the unit cube Id is a Schauder basis in the classical Besov space Bsp,q,1(Id), 0 < p < 1, defined by first order differences in the limiting case s = d(1/p − 1), if and only if 0 < q ≤ p. For d = 1 and p < q < ∞, this settles the only open case in our 1979 paper [4], where the Schauder basis property of H in Bsp,q,1(I) for 0 < p < 1 was left undecided. We also consider the Schauder basis property of Hd for the standard Besov spaces Bsp,q(Id) defined by Fourier-analytic methods in the limiting cases s = d(1/p−1) and s = 1, complementing results by Triebel [7].},
url = {https://hdl.handle.net/20.500.11811/11812}
}
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