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.

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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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