Espaços de Hardy radial

Abstract

One presents in this work an atomic decomposition via radial atoms for distributions on subspace $\mathcal{H}^{p}_{rad}(\mathds{R}^{n})$ for $0 < p\leqslant 1$, of Hardy radial spaces $H_{rad}^{p}(\mathds{R}^{n}) \doteq H^{p}(\mathds{R}^{n}) \cap \mathcal{S}'_{rad}(\mathds{R}^n)$. Such atomic decomposition tell us that, if $f \in \mathcal{H}^{p}_{rad}(\mathds{R}^{n})\subseteq H_{rad}^{p}(\mathds{R}^n)$, then $f$ has an atomic decomposition and the atoms of its decomposition are radials.

This work extends a theorem proved by R. R. Coifman and G. Weiss in which the authors give a radial atomic decomposition for radial functions in $H^1(\mathds{R}^n)$ where the atoms of such decomposition are radial functions.

The decomposition that we present here give us similar about the atoms radiallity for $0<p\leqslant 1$. Specifically we define a maximal radial Hardy space and we prove an atomic decomposition for this spaces via radial atoms