Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Basis of wavelets and atomic decompositions of $ H\sp 1({\bf R}\sp n)$ and $ H\sp 1({\bf R}\sp n\times {\bf R}\sp n)$

Authors: J. Aguirre, M. Escobedo, J. C. Peral and Ph. Tchamitchian
Journal: Proc. Amer. Math. Soc. 111 (1991), 683-693
MSC: Primary 42C15; Secondary 42B30
MathSciNet review: 1050015
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Abstract: It is shown that, as in the case of $ {H^1}({\mathbb{R}^n})$ and $ {\text{BMO(}}{\mathbb{R}^n})$, wavelets provide unconditional basis of $ {H^1}({\mathbb{R}^n} \times \mathbb{R}n)$ and $ {\text{BMO(}}{\mathbb{R}^n} \times \mathbb{R}n)$. Moreover, we show how wavelets can be used to obtain the usual atomic decompositions in $ {H^1}{\text{(}}{\mathbb{R}^n})$ and $ {H^1}{\text{(}}{\mathbb{R}^n} \times \mathbb{R}n)$.

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Keywords: Atomic decomposition, Hardy space, wavelet
Article copyright: © Copyright 1991 American Mathematical Society