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 
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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

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