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The Singularity Property of Banach Function Spaces and Unconditional Convergence in L 1[0, 1]

The Singularity Property of Banach Function Spaces and Unconditional Convergence in L 1[0, 1] Let X be a Banach function space, L ∞ [0, 1] ⊂ X ⊂ L 1[0, 1]. It is proved that if dual space of X has singularity property in closed set E ⊂ [0, 1] then: 1) there exists no orthonormal basis in C[0, 1], which forms an unconditional basis in X in metric of L 1[0, 1] space, 2) for the Hardy-Littlewood maximal operator M we have [InlineMediaObject not available: see fulltext.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

The Singularity Property of Banach Function Spaces and Unconditional Convergence in L 1[0, 1]

Kopaliani, Tengizi S.
Positivity , Volume 10 (3) – May 24, 2006
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References (4)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Birkhäuser Verlag, Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
DOI
10.1007/s11117-005-0001-6
Publisher site
See Article on Publisher Site

Abstract

Let X be a Banach function space, L ∞ [0, 1] ⊂ X ⊂ L 1[0, 1]. It is proved that if dual space of X has singularity property in closed set E ⊂ [0, 1] then: 1) there exists no orthonormal basis in C[0, 1], which forms an unconditional basis in X in metric of L 1[0, 1] space, 2) for the Hardy-Littlewood maximal operator M we have [InlineMediaObject not available: see fulltext.]

Journal

Positivity – Springer Journals

Published: May 24, 2006

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