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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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{\textendash}Lorentz} classes $H^{1,q}$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--167},
     year = {2005},
     volume = {327},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_327_a9/}
}
TY  - JOUR
AU  - D. V. Parilov
TI  - Two theorems on the Hardy–Lorentz classes $H^{1,q}$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 150
EP  - 167
VL  - 327
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_327_a9/
LA  - ru
ID  - ZNSL_2005_327_a9
ER  - 
%0 Journal Article
%A D. V. Parilov
%T Two theorems on the Hardy–Lorentz classes $H^{1,q}$
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 150-167
%V 327
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_327_a9/
%G ru
%F ZNSL_2005_327_a9
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/

[1] J. Garcia-Cuerva, J. L. Rubio de Francia, Weighted norm inequalities and related topics, North–Holland, 1986

[2] R. Fefferman, F. Soria, “The space Weak $H^1$”, Studia Mathematica, 85:1 (1986), 1–16 | MR | Zbl

[3] F. J. Ruiz, J. L. Torrea, “Calderón–Zygmund theory for operator-valued kernels”, Advances in Mathematics, 62:1 (1986), 1–46 | DOI | MR

[4] A. Torchinsky, Real-variable methods in harmonic analysis, Academic Press, Inc., 1986 | MR | Zbl

[5] I. Stein, Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR