Year: 2026
Type: preprint
Abstract: We quantify the failure of interpolation between Hardy spaces $H^p(\mathbb T^\infty)$ on the infinite-dimensional torus. For any set $A\subseteq[1,\infty]$ such that $A\setminus\{\infty\}$ is closed in $[1,\infty)$, we show that there exists an operator that is densely defined on $H^p(\mathbb T^\infty)$ for all $1\leq p<\infty$ and weak-$\ast$ densely defined on $H^\infty(\mathbb T^\infty)$ that extends to a bounded linear operator on $H^p(\mathbb T^\infty)$ if and only if $p\in A$.
Source: arXiv (Cornell University)
Author: Andersson, Viktor
Institution: Norwegian University of Science and Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Norges Forskningsråd
OpenAlex ID: W7212517752