Geodesic
A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions
Adam Osękowski1
1 Faculty of Mathematics, Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 3, pp. 261-274.

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

Let $X$ be a submartingale starting from $0$, and $Y$ be a semimartingale which is orthogonal and strongly differentially subordinate to $X$. The paper contains the proof of the sharp estimate $$ \mathbb{P}\left(\sup_{t\geq 0}|Y_t|\geq 1\right)\leq 3.375\ldots \|X\|_1. $$ As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.
DOI : 10.4064/ba59-3-7
Keywords: submartingale starting semimartingale which orthogonal strongly differentially subordinate paper contains proof sharp estimate mathbb sup geq geq right leq ldots application related weak type inequality smooth functions euclidean domains established

Adam Osękowski 1

1 Faculty of Mathematics, Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland 
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Adam Osękowski. A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 3, pp. 261-274. doi : 10.4064/ba59-3-7. http://geodesic.mathdoc.fr/articles/10.4064/ba59-3-7/

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