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.]
Positivity – Springer Journals
Published: May 24, 2006
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