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Exotic operators on the Hardy spaces of the infinite-dimensional torus
Abstract
We quantify the failure of interpolation between Hardy spaces Hp(πβ) on the infinite-dimensional torus. For any set Aβ[1,β] such that Aβ{β} is closed in [1,β), we show that there exists an operator that is densely defined on Hp(πβ) for all 1β€ p<β and weak-β densely defined on Hβ(πβ) that extends to a bounded linear operator on Hp(πβ) if and only if pβ A.
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BibTeX
@misc{andersson2026exotic,
title = {{Exotic operators on the Hardy spaces of the infinite-dimensional torus}},
author = {Viktor Andersson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12859},
eprint = {2609.12859},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12859},
}
RIS
TY - UNPB
TI - Exotic operators on the Hardy spaces of the infinite-dimensional torus
AU - Viktor Andersson
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12859
UR - https://arxiv.org/abs/2609.12859
AB - We quantify the failure of interpolation between Hardy spaces H^p(π^β) on the infinite-dimensional torus. For any set Aβ[1,β] such that Aβ{β} is closed in [1,β), we show that there exists an operator that is densely defined on H^p(π^β) for all 1β€ p<β and weak-β densely defined on H^β(π^β) that extends to a bounded linear operator on H^p(π^β) if and only if pβ A.
ER -