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- W1606280557 abstract "Let $X$ be a supermartingale starting from $0$ which has only nonnegative jumps. For each $0<p<1$ we determine the best constants $c_p$, $C_p$ and $mathfrak{c}_p$ such that $$ ,,,,sup_{tgeq 0}left|left|X_tright|right|_pleq C_pleft|left|-inf_{tgeq 0}X_tright|right|_p,$$ $$ ,,||sup_{tgeq 0}X_t||_pleq c_pleft|left|-inf_{tgeq 0}X_tright|right|_p$$ and $$ ||sup_{tgeq 0}|X_t|;||_pleq mathfrak{c}_pleft|left|-inf_{tgeq 0}X_tright|right|_p.$$ The estimates are shown to be sharp if $X$ is assumed to be a stopped one-dimensional Brownian motion. The inequalities are deduced from the existence of special functions, enjoying certain majorization and convexity-type properties. Some applications concerning harmonic functions on Euclidean domains are indicated." @default.
- W1606280557 created "2016-06-24" @default.
- W1606280557 creator A5066168271 @default.
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- W1606280557 date "2013-12-18" @default.
- W1606280557 modified "2023-10-18" @default.
- W1606280557 title "Sharp maximal $L^p$-estimates for martingales" @default.
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