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Bulletin of the London Mathematical Society Advance Access published online on April 23, 2008
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdn022
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© 2008 London Mathematical Society

Haar type and Carleson constants

Stefan Geiss

Department of Mathematics and Statistics
University of Jyväskylä
PO Box 35 (MaD)
FIN-40014
Finland

Paul F. X. Müller

Department of Analysis
J.Kepler University
A-4040 Linz
Austria

Received 26 February 2007. Revision received 5 January 2007.

For a collection E of dyadic intervals, a Banach space X, and pisin(1, 2], we assume the upper {ell}p estimates Formula

where xIisinX, and hI denotes the L{infty} normalized Haar function supported on I. We determine the minimal requirement on the size of E such that these estimates imply that X is of Haar type p. The characterization is given in terms of the Carleson constant of E.

2000 Mathematics Subject Classification 46B07, 46B20.

Research of both authors supported in part by FWF Pr. Nr. P150907-N01.


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