Hardy Spaces and Beurling Algebras

Abstract

We extend the results of Chen and Lau [2] in two directions. First we work on Rn whereas the setting of [2] is the real line. Secondly we obtain atomic decompositions for the whole range 1 < p < ∞, going beyond the decomposition obtained in [2], which was only valid for 1 < p ⩽ 2. Our method is simpler than that used in [2] and is based upon a different principle: the characterization by the ‘grand maximal function’.