Sharp Lp Estimates on BMO

被引：31

作者：

Slavin, Leonid ^{[1
]}

Vasyunin, Vasily ^{[2
]}

机构：

[1] Univ Cincinnati, Cincinnati, OH 45221 USA

[2] RAS, VA Steldov Math Inst, St Petersburg Dept, Moscow, Russia

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2012年 / 61卷 / 03期

基金：

美国国家科学基金会;

关键词：

BMO; norm equivalence; explicit Bellman function; Monge-Ampere equation; BELLMAN FUNCTIONS; MAXIMAL OPERATORS; INEQUALITIES;

D O I：

10.1512/iumj.2012.61.4651

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct the upper and lower Bellman functions for the L-p (quasi)-norms of BMO functions. These appear as solution to a series of Monge-Ampere boundary value problems on a non-convex plane domain. The knowledge of the Bellman functions leads to sharp constants in inequalities relating average oscillations of BMO functions and various BMO norms.

引用

页码：1051 / 1110

页数：60

共 21 条

[1]

BELLMAN R., 2010, DYNAMIC PROGRAMMING

[2] BOUNDARY-VALUE-PROBLEMS AND SHARP INEQUALITIES FOR MARTINGALE TRANSFORMS [J].