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arXiv · 1506.02202

Estimates for the Corona Theorem on $H^{\infty}_{\mathbb{I}}(\D)$

Debendra P. Banjade
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Abstract

Let $\mathbb{I}$ be a proper ideal of $H^{\infty}(\D)$. We prove the corona theorem for infinitely many generators on the algebra $H^{\infty}_{\mathbb{I}}$ in which the corona theorem for finitely many functions is known to hold. This settles the conjecture of Ryle \cite{ryle1}. We also provide the estimates for corona solutions. Moreover, we prove a generalized Wolff's Ideal Theorem for this sub-algebra.

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BibTeXRIS

Debendra P. Banjade. 2015-06-06. Estimates for the Corona Theorem on $H^{\infty}_{\mathbb{I}}(\D)$. https://arxiv.org/abs/1506.02202

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