Geodesic
Martingale operators and Hardy spaces generated by them
Studia Mathematica, Tome 114 (1995) no. 1, pp. 39-70

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Martingale Hardy spaces and BMO spaces generated by an operator T are investigated. An atomic decomposition of the space $H_{p}^{T}$ is given if the operator T is predictable. We generalize the John-Nirenberg theorem, namely, we prove that the $BMO_q$ spaces generated by an operator T are all equivalent. The sharp operator is also considered and it is verified that the $L_p$ norm of the sharp operator is equivalent to the $H_{p}^{T}$ norm. The interpolation spaces between the Hardy and BMO spaces are identified by the real method. Martingale inequalities between Hardy spaces generated by two different operators are considered. In particular, we obtain inequalities for the maximal function, for the q-variation and for the conditional q-variation. The duals of the Hardy spaces generated by these special operators are characterized.
DOI : 10.4064/sm-114-1-39-70

Ferenc Weisz 1

1 
@article{10_4064_sm_114_1_39_70,
     author = {Ferenc Weisz},
     title = {Martingale operators and {Hardy} spaces generated by them},
     journal = {Studia Mathematica},
     pages = {39--70},
     publisher = {mathdoc},
     volume = {114},
     number = {1},
     year = {1995},
     doi = {10.4064/sm-114-1-39-70},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-114-1-39-70/}
}
TY  - JOUR
AU  - Ferenc Weisz
TI  - Martingale operators and Hardy spaces generated by them
JO  - Studia Mathematica
PY  - 1995
SP  - 39
EP  - 70
VL  - 114
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-114-1-39-70/
DO  - 10.4064/sm-114-1-39-70
LA  - en
ID  - 10_4064_sm_114_1_39_70
ER  - 
%0 Journal Article
%A Ferenc Weisz
%T Martingale operators and Hardy spaces generated by them
%J Studia Mathematica
%D 1995
%P 39-70
%V 114
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-114-1-39-70/
%R 10.4064/sm-114-1-39-70
%G en
%F 10_4064_sm_114_1_39_70
Ferenc Weisz. Martingale operators and Hardy spaces generated by them. Studia Mathematica, Tome 114 (1995) no. 1, pp. 39-70. doi: 10.4064/sm-114-1-39-70

Cité par Sources :