A partial differential equation characterization of anisotropic Hardy spaces

We obtain a differential characterization for the anisotropic Hardy space HAp$H_A^p$ by identifying it with a parabolic Hardy space associated with a general continuous group. This allows HAp$H_A^p$ to be defined using a parabolic differential equation of Calderón and Torchinsky. We also provide a c...

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Bibliographic Details
Published in:Mathematische Nachrichten 2023-06, Vol.296 (6), p.2258-2275
Main Authors: Bownik, Marcin, Wang, Li‐An Daniel
Format: Article
Language:English
Subjects:
anisotropic Hardy spaces
continuous groups of dilations
Linear transformations
Parabolic differential equations
parabolic Hardy spaces
Partial differential equations
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Summary:We obtain a differential characterization for the anisotropic Hardy space HAp$H_A^p$ by identifying it with a parabolic Hardy space associated with a general continuous group. This allows HAp$H_A^p$ to be defined using a parabolic differential equation of Calderón and Torchinsky. We also provide a classification of dilations corresponding to equivalent anisotropic Hardy spaces with respect to linear transformations.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202100368