期刊论文详细信息
Canadian mathematical bulletin | |
Sharp Inequalities for Differentially Subordinate Harmonic Functions and Martingales | |
Adam Osękowski1  | |
[1] Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland | |
关键词: harmonic function; conjugate harmonic functions; orthogonal harmonic functions; martingale; orthogonal martingales; norm inequality; optimal stopping problem; | |
DOI : 10.4153/CMB-2011-113-8 | |
学科分类:数学(综合) | |
来源: University of Toronto Press * Journals Division | |
【 摘 要 】
We determine the best constants $C_{p,infty}$ and $C_{1,p}$,$1 < p < infty$, for which the following holds. If $u$, $v$ areorthogonal harmonic functions on a Euclidean domain such that $v$ isdifferentially subordinate to $u$, then $$ |v|_p leq C_{p,infty}|u|_infty,quad|v|_1 leq C_{1,p} |u|_p.$$In particular, the inequalities are still sharp for the conjugateharmonic functions on the unit disc of $mathbb R^2$. Sharp probabilistic versions of these estimates are also studied. As an application, we establish a sharp version of the classical logarithmic inequality of Zygmund.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912050576888ZK.pdf | 37KB | download |