通过消失 Carleson 测度对 VMO 的分解与刻画
复变函数
2026-03-18 v2
摘要
我们建立了 关于消失 Carleson 测度的两种等价刻画。首先，我们证明任意 函数可分解为一个连续边界项与一个由消失 Carleson 测度相伴的积分算子。其次，受 Varopoulos 关于 -方程工作的启发，我们通过其梯度诱导消失 Carleson 测度的光滑函数的边界值刻画了 。作为推论，我们重新得到了已知表示 从而为此分解提供了新视角。
引用
@article{arxiv.2309.06155,
title = {Decomposition and characterization of VMO via vanishing Carleson measures},
author = {Fei Tao and Yaosong Yang},
journal= {arXiv preprint arXiv:2309.06155},
year = {2026}
}
备注
Major revision. Author list updated. After a substantial revision of the paper, some sections and results related to the higner dimentional case have been removed in order to maintain the coherence of the presentation. Consequently, the author list has been adjusted accordingly, with the agreement of all authors