From dyadic ${\mathrm{\Lambda }}_{\alpha }$ to ${\mathrm{\Lambda }}_{\alpha }$

In this paper we show how to compute the ${\mathrm{\Lambda }}_{\alpha }$ norm, $\alpha\ge 0$, using the dyadic grid. This result is a consequence of the description of the Hardy spaces $H^p(R^N)$ in terms of dyadic and special atoms.