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Hardy and BMO spaces on Weyl chambers

  • Paweł Plewa ORCID logo EMAIL logo and Krzysztof Stempak ORCID logo
Published/Copyright: August 25, 2023

Abstract

Let W be a finite reflection group associated with a root system R in 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 Hom ( W , ^ 2 ) which attaches the ± signs to the facets of C + . Specialized to orthogonal root systems, atomic decompositions in H η 1 and h η 1 are obtained and the duality problem is also treated.

MSC 2020: 46E30; 42B30

Communicated by Christopher D. Sogge


Funding statement: P. Plewa acknowledges the financial support of Compagnia di San Paolo.

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Received: 2023-05-22
Revised: 2023-06-25
Published Online: 2023-08-25
Published in Print: 2024-01-01

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