On functions of bounded mean oscillation with bounded negative part

IF 0.6 3区数学 Q3 MATHEMATICS Analysis Mathematica Pub Date : 2024-04-30 DOI:10.1007/s10476-024-00018-9

H. Zhao, D. Wang

引用次数: 0

Abstract

Let $b$ be a locally integrable function and $\mathfrak{M}$ be the bilinear maximal function

$$\mathfrak{M}(f,g)(x)=\sup_{Q\ni x}\frac{1}{|Q|}\int_{Q}|f(y)g(2x-y)|dy.$$

In this paper, characterization of the BMO function in terms of commutator $\mathfrak{M}^{(1)}_{b}$ is established. Also, we obtain the necessary and sufficient conditions for the boundedness of the commutator $[b, \mathfrak{M}]_{1}$. Moreover, some new characterizations of Lipschitz and non-negative Lipschitz functions are obtained.

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关于具有有界负部分的有界平均振荡函数

设 $b$ 是局部可积分函数，$\mathfrak{M}$ 是双线性最大函数$$\mathfrak{M}(f,g)(x)=\sup_{Q\ni x}\frac{1}{|Q}\int_{Q}|f(y)g(2x-y)|dy.本文建立了换元器 $\mathfrak{M}^{(1)}_{b}$对 BMO 函数的描述。同时，我们还得到了换元 $[b, \mathfrak{M}]_{1}$ 有界的必要条件和充分条件。此外，我们还得到了一些关于 Lipschitz 函数和非负 Lipschitz 函数的新特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.

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