The Haar System in Triebel-Lizorkin Spaces: Endpoint Results

Abstract

We characterize the Schauder and unconditional basis properties for the Haar system in the Triebel-Lizorkin spaces $F_{p,q}^s({\mathbb{R}}^d)$, 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].

Minor revision. To appear in Journal of Geometric Analysis