A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions

摘要

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 P(sup_(t≥0) |Y_t| ≥ l) ≤ 3.375... ‖X‖_1. As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.