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On the asymptotic growth of the norm of the partial sum operator on ℋ1
Abstract
We show that the norm of the partial sum operator SN on the Hardy space ℋ1 of Dirichlet series satisfies liminfN→∞(loglog N)/(log N)lVert SNrVertℋ1→ℋ1≥(1−log 2)/2π. Combined with an upper bound of Bondarenko, Brevig, Saksman and Seip, this shows that lVert SNrVertℋ1→ℋ1asymp(log N)/(loglog N) as N→∞.
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BibTeX
@misc{andersson2026asymptotic,
title = {{On the asymptotic growth of the norm of the partial sum operator on $\mathscr H^1$}},
author = {Viktor Andersson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23666},
eprint = {2610.23666},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23666},
}
RIS
TY - UNPB
TI - On the asymptotic growth of the norm of the partial sum operator on ℋ^1
AU - Viktor Andersson
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23666
UR - https://arxiv.org/abs/2610.23666
AB - We show that the norm of the partial sum operator S_N on the Hardy space ℋ^1 of Dirichlet series satisfies liminf_N→∞(loglog N)/(log N)lVert S_NrVert_ℋ^1→ℋ^1≥(1−log 2)/2π. Combined with an upper bound of Bondarenko, Brevig, Saksman and Seip, this shows that lVert S_NrVert_ℋ^1→ℋ^1asymp(log N)/(loglog N) as N→∞.
ER -