Geodesic
Two theorems on the Hardy--Lorentz classes $H^{1,q}$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 33, Tome 327 (2005), pp. 150-167

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In this paper two main topics are described. First, we obtain atomic decomposition for the spaces $H^{1,q}$, $1$ (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 $H^{(1,\infty)}$. 
@article{ZNSL_2005_327_a9,
     author = {D. V. Parilov},
     title = {Two theorems on the {Hardy--Lorentz} classes $H^{1,q}$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--167},
     publisher = {mathdoc},
     volume = {327},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_327_a9/}
}
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D. V. Parilov. Two theorems on the Hardy--Lorentz classes $H^{1,q}$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 33, Tome 327 (2005), pp. 150-167. http://geodesic.mathdoc.fr/item/ZNSL_2005_327_a9/