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The Haar System in Triebel-Lizorkin Spaces: Endpoint Results

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arxiv 1907.03738 v2 pith:OHRRZTYU submitted 2019-07-08 math.CA cs.NAmath.FAmath.NA

classification math.CAcs.NAmath.FAmath.NA
keywords spacestriebel-lizorkinendpointhaarpropertiesresultssystembasis
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abstract

We characterize the Schauder and unconditional basis properties for the Haar system in the Triebel-Lizorkin spaces $F^s_{p,q}(\Bbb R^d)$, at the endpoint cases $s=1$, $s=d/p-d$ and $p=\infty$. Together with the earlier results in [10], [4], this completes the picture for such properties in the Triebel-Lizorkin scale, and complements a similar study for the Besov spaces given in [5].

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