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Diagonal operators on Janson-Sobolev and Janson-Sobolev-Hardy spaces
Abstract
We study the Banach space and operator factorization structure of Janson-Sobolev and Janson-Sobolev-Hardy spaces. This new class of martingale spaces is determined by a q-adic filtration, a subspace V⊂ ℝ0l× q, and a rearrangement invariant function space X. Our main result shows that, for every bounded diagonal operator D, the operator S = ∑t=1s λ𝒰kt(D)Q𝒦tℬ determined by the linear functionals λ𝒰kt(D) and the canonical projections Q𝒦tℬ, almost projectionally factors through D with constant 1+. As consequences, we obtain factorization results for diagonal operators both under a natural boundedness condition on the canonical projections and for all spaces equipped with the L1-norm.
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BibTeX
@misc{kazaniecki2026diagonal,
title = {{Diagonal operators on Janson-Sobolev and Janson-Sobolev-Hardy spaces}},
author = {Krystian Kazaniecki and Richard Lechner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01628},
eprint = {2610.01628},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01628},
}
RIS
TY - UNPB
TI - Diagonal operators on Janson-Sobolev and Janson-Sobolev-Hardy spaces
AU - Krystian Kazaniecki
AU - Richard Lechner
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01628
UR - https://arxiv.org/abs/2610.01628
AB - We study the Banach space and operator factorization structure of Janson-Sobolev and Janson-Sobolev-Hardy spaces. This new class of martingale spaces is determined by a q-adic filtration, a subspace V⊂ ℝ_0^l× q, and a rearrangement invariant function space X. Our main result shows that, for every bounded diagonal operator D, the operator S = ∑_t=1^s λ_𝒰^k_t(D)Q_𝒦_t^ℬ determined by the linear functionals λ_𝒰^k_t(D) and the canonical projections Q_𝒦_t^ℬ, almost projectionally factors through D with constant 1^+. As consequences, we obtain factorization results for diagonal operators both under a natural boundedness condition on the canonical projections and for all spaces equipped with the L^1-norm.
ER -