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Estimates in corona theorems for some subalgebras of$H$^{∞}

Amol Sasane Department of Mathematics, London School of Economics Sergei Treil Mathematics Department, Brown University

TBD mathscidoc:1701.333109

Arkiv for Matematik, 45, (2), 351-380, 2006.9
If$n$is a non-negative integer, then denote by ∂^{-$n$}$H$^{∞}the space of all complex-valued functions$f$defined on $\mathbb{D}$ such that$f$,$f$^{(1)},$f$^{(2)},...,$f$^{($n$)}belong to$H$^{∞}, with the norm $$\|f\|=\sum_{j=0}^{n}\frac{1}{j!}\|f^{(j)}\|_{\infty}.$$ We prove bounds on the solution in the corona problem for ∂^{-$n$}$H$^{∞}. As corollaries, we obtain estimates in the corona theorem also for some other subalgebras of the Hardy space$H$^{∞}.
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@inproceedings{amol2006estimates,
  title={Estimates in corona theorems for some subalgebras of$H$^{∞}},
  author={Amol Sasane, and Sergei Treil},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620296564918},
  booktitle={Arkiv for Matematik},
  volume={45},
  number={2},
  pages={351-380},
  year={2006},
}
Amol Sasane, and Sergei Treil. Estimates in corona theorems for some subalgebras of$H$^{∞}. 2006. Vol. 45. In Arkiv for Matematik. pp.351-380. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620296564918.
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