Two theorems on the Hardy–Lorentz classes $H^{1,q}$

In this paper two main topics are described. First, we obtain atomic decomposition for the spaces $H^{1,q}$, $1<q<\infty$ (this case has not been considered before). Second, we show that a multiplier that meets the condition of the Marcinkiewicz Theorem, acts from $H^1$ to $H^{(1,\infty)}$.