Speaker
Evgueni Doubtsov
(St. Petersburg Department of V.A. Steklov Mathematical Institute)
Description
Let $H^2 = H^2(B_n)$ denote the standard Hardy space on the open unit ball $B_n$ of $\mathbb{C}^n$, $n\ge 2$, and let $\sigma$ denote the normalized Lebesgue measure on the unit sphere $\partial B_n$. Given an inner function $I$, a Lebesgue measurable set $E\subset \partial B_n$ is said to be dominant for the large model space $H^2 \ominus I H^2$ if $\sigma(E) < 1$ and $\|f\|_{H^2}^2 \le C\int_E |f|^2\, d\sigma$ for all $f\in H^2 \ominus I H^2$. We use Clark measures to construct dominant sets for an arbitrary inner function. This research was supported by Russian Science Foundation (grant No. 19-11-00058).
Primary author
Evgueni Doubtsov
(St. Petersburg Department of V.A. Steklov Mathematical Institute)
Co-author
Prof.
Aleksei B. Aleksandrov
(St. Petersburg Department of V.A. Steklov Mathematical Institute)
