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A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions

Tom 59 / 2011

Adam Osękowski Bulletin Polish Acad. Sci. Math. 59 (2011), 261-274 MSC: Primary 60G44; Secondary 31B05. DOI: 10.4064/ba59-3-7

Streszczenie

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.

Autorzy

  • Adam OsękowskiFaculty of Mathematics, Informatics and Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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