Year: 2026
Type: preprint
Abstract: Bayart, Pellegrino, and Rueda obtained diagonal absolute summability exponents for continuous \(m\)-linear operators from \((\ell_1)^m\) into \(\ell_p\). Their optimality was known for \(2\le p\le\infty\), whereas the case \(1\le p<2\) remained open. We settle the latter case by means of finite Walsh test operators, and consequently obtain the optimal exponent for every \(1\le p\le\infty\). The same argument, combined with the corresponding interpolation and embedding results, also yields optimal Kwapień-type statements for several related range spaces.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204864878