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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
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Abstract

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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

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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