PreprintarXiv licencearXiv
Optimality in a Multilinear Extension of Kwapień's Theorem
Abstract
Bayart, Pellegrino, and Rueda obtained diagonal absolute summability exponents for continuous m-linear operators from (ℓ1)m into ℓp. Their optimality was known for 2≤ p≤∞, whereas the case 1≤ p<2 remained open. We settle the latter case by means of finite Walsh test operators, and consequently obtain the optimal exponent for every 1≤ p≤∞. The same argument, combined with the corresponding interpolation and embedding results, also yields optimal Kwapień-type statements for several related range spaces.
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BibTeX
@misc{castanomarin2026optimality,
title = {{Optimality in a Multilinear Extension of Kwapień's Theorem}},
author = {Luis Miguel Castaño-Marín and Geivison Ribeiro and Diana Serrano-Rodríguez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.29443},
eprint = {2608.29443},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29443},
}
RIS
TY - UNPB
TI - Optimality in a Multilinear Extension of Kwapień's Theorem
AU - Luis Miguel Castaño-Marín
AU - Geivison Ribeiro
AU - Diana Serrano-Rodríguez
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2608.29443
UR - https://arxiv.org/abs/2608.29443
AB - Bayart, Pellegrino, and Rueda obtained diagonal absolute summability exponents for continuous m-linear operators from (ℓ_1)^m into ℓ_p. Their optimality was known for 2≤ p≤∞, whereas the case 1≤ p<2 remained open. We settle the latter case by means of finite Walsh test operators, and consequently obtain the optimal exponent for every 1≤ p≤∞. The same argument, combined with the corresponding interpolation and embedding results, also yields optimal Kwapień-type statements for several related range spaces.
ER -