Geodesic
Weak Type Inequality for the Square Function of a Nonnegative Submartingale
Adam Os/ekowski1
1 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 1, pp. 81-89.

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

Let $f$ be a nonnegative submartingale and $S(f)$ denote its square function. We show that for any $\lambda>0$, $$ \lambda \mathbb{P}(S(f)\geq \lambda) \leq \frac{\pi}{2}\,\|f\|_1,$$ and the constant $\pi/2$ is the best possible. The inequality is strict provided $\|f\|_1\neq 0$.
DOI : 10.4064/ba57-1-9
Keywords: nonnegative submartingale denote its square function lambda lambda mathbb geq lambda leq frac constant best possible inequality strict provided neq

Adam Os/ekowski 1

1 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland 
@article{10_4064_ba57_1_9,
     author = {Adam Os/ekowski},
     title = {Weak {Type} {Inequality} for the {Square} {Function} of a {Nonnegative} {Submartingale}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {81--89},
     publisher = {mathdoc},
     volume = {57},
     number = {1},
     year = {2009},
     doi = {10.4064/ba57-1-9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba57-1-9/}
}
TY  - JOUR
AU  - Adam Os/ekowski
TI  - Weak Type Inequality for the Square Function of a Nonnegative Submartingale
JO  - Bulletin of the Polish Academy of Sciences. Mathematics
PY  - 2009
SP  - 81
EP  - 89
VL  - 57
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba57-1-9/
DO  - 10.4064/ba57-1-9
LA  - en
ID  - 10_4064_ba57_1_9
ER  - 
%0 Journal Article
%A Adam Os/ekowski
%T Weak Type Inequality for the Square Function of a Nonnegative Submartingale
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2009
%P 81-89
%V 57
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ba57-1-9/
%R 10.4064/ba57-1-9
%G en
%F 10_4064_ba57_1_9
Adam Os/ekowski. Weak Type Inequality for the Square Function of a Nonnegative Submartingale. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 1, pp. 81-89. doi : 10.4064/ba57-1-9. http://geodesic.mathdoc.fr/articles/10.4064/ba57-1-9/

Cité par Sources :