Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T19:00:05.224Z Has data issue: false hasContentIssue false
  • English
  • Français

A Remark on Bases in Hardy Spaces

Published online by Cambridge University Press:  20 November 2018

Peter Sjögren
Peter Sjögren*
Affiliation:
Department of Mathematics, Chalmers University of Technology, University of Göteborg, S-412 96 Göteborg, Sweden
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Franklin spline system in [0,1] has been generalized by Strömberg to a system in ℝn which is an unconditional basis in Hp(ℝn) for p > n/(n + m +1). Here the natural number m is the order of the system. For some of these values of p, it was known that the Hp quasi-norm is equivalent to a certain expression containing the coefficients of the function with respect to this basis. We prove this equivalence for all p > n/(n + m +1).

Keywords

42C1042B30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 360 - 364
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Calderón, A. P. and Torchinsky, A., Parabolic maximal functions associated with a distribution. Adv. in Math. 16 (1975), 1–64.Google Scholar
2. Sjölin, P. and Strômberg, J.-O., Basis properties of Hardy spaces, Ark. Mat. 21 (1983), 111–125.Google Scholar
3. Sjölin, P. and Strömberg, J.-O., Spline systems as bases in Hardy spaces, Israel J. Math., 45 (1983), 147–156.Google Scholar
4. Strômberg, J.-O., A modified Franklin system and higher spline systems on Un as unconditional bases of Hardy spaces, in Conference on Harmonic Analysis in honour of Antoni Zygmund. Beckner (ed.) Wadsworth 1982, 475–494.Google Scholar