Theory of locally concave functions and its applications to sharp estimates of integral functionals

被引：18

作者：

Stolyarov, D. M. ^{[1
]}

Zatitskiy, P. B. ^{[1
]}

机构：

[1] St Petersburg State Univ, Russian Acad Sci, St Petersburg Dept Steklov Math Inst, PL Chebyshev Res Lab, St Petersburg 199034, Russia

来源：

ADVANCES IN MATHEMATICS | 2016年 / 291卷

基金：

俄罗斯科学基金会;

关键词：

Bellman function; Integral functional; BMO; Muckenhoupt class; Monotonic rearrangement; BELLMAN FUNCTION; INEQUALITIES;

D O I：

10.1016/j.aim.2015.11.048

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of martingales and an extremal problem on this class, which is dual to the minimization problem for locally concave functions. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：228 / 273

页数：46

共 40 条

[1]

[Anonymous], 1956, Ark. Mat, DOI 10.1007/BF02589410

[2]

Beznosova O., 2014, ALGEBR ANAL, V26, P40

[3] THE MUCKENHOUPT CLASS A1(R) [J].