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arXiv · 1901.09117

Basis properties of the Haar system in limiting Besov spaces

Gustavo Garrigós·Andreas Seeger·Tino Ullrich
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Abstract

We study Schauder basis properties for the Haar system in Besov spaces $B^s_{p,q}(\mathbb{R}^d)$. We give a complete description of the limiting cases, obtaining various positive results for $q\leq \min\{1,p\}$, and providing new counterexamples in other situations. The study is based on suitable estimates of the dyadic averaging operators $\mathbb{E}_N$; in particular we find asymptotically optimal growth rates for the norms of these operators in global and local situations.

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Gustavo Garrigós, Andreas Seeger, Tino Ullrich. 2019-01-25. Basis properties of the Haar system in limiting Besov spaces. https://doi.org/10.1007/978-3-030-72058-2%5C_11

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