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arXiv · 2304.13533

Hardy and BMO spaces on Weyl chambers

Paweł Plewa·Krzysztof Stempak
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Abstract

Let $W$ be a finite reflection group associated with root system $R$ in $\mathbb R^d$. Let $C_+$ denote a positive Weyl chamber distinguished by a choice of $R_+$, a set of positive roots. We define and investigate Hardy and BMO spaces on $C_+$ in the framework of boundary conditions given by a homomorphism $η\in\mathrm{Hom}(W,\hat{\mathbb{Z}}_2)$ which attaches the $\pm$ signs to the facets of $C_+$. Specialized to orthogonal root systems, atomic decompositions in $H^1_η$ and $h^1_η$ are obtained and the duality problem is also treated.

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Paweł Plewa, Krzysztof Stempak. 2023-04-26. Hardy and BMO spaces on Weyl chambers. https://doi.org/10.1515/forum-2023-0192

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