某些 $H^\infty$ 子代数的 corona 定理中的估计
经典分析与常微分方程
2010-07-08 v1 泛函分析
摘要
我们得到单位圆盘内其 n 阶导数有界的解析函数代数及其由 n 阶导数边界连续性所定义的子代数的 corona 定理中的估计。此类代数的 corona 定理是平凡且已知的,但带估计的 corona 定理是新的且证明起来困难得多。作为一个独立有意义的辅助结果,我们得到了此类代数(包括有界解析函数代数 的经典情形)中最佳估计的连续性。我们还表明,对固定的 ,我们所考虑的所有代数中的最佳估计是相同的。
引用
@article{arxiv.math/0702754,
title = {Estimates in corona theorems for some subalgebras of $H^\infty$},
author = {Amol Sasane and Sergei Treil},
journal= {arXiv preprint arXiv:math/0702754},
year = {2010}
}
备注
24 pages, 1 postscript figure. A preliminary version of this paper is available as LSE report LSE-CDAM-2006-09, see http://www.cdam.lse.ac.uk/Reports/Files/cdam-2006-09.pdf The difference with the preliminary version: minor errors/typos pointed by referee are corrected; connection with earlier work of V. Tolokonnikov is clarified; section 2.5 explaining known facts about Carleson measures is added