The zero sets of ℓAp are nested

Abstract

It is shown by construction that if $1<p_1<p_2<\infty$, then there exists a sequence of points in the open unit disk that is a zero set for ${\ell }_A^{p_2}$ but not for ${\ell }_A^{p_1}$. The proof utilizes a zero set criterion for ${\ell }_A^p$ based on a notion of $p$-inner functions.