Year: 2026
Type: preprint
Abstract: For every $22$, both estimates in Talagrand's Research Problem~2.11.3 fail in each of the spaces $L^p[0,1]$ and $\ell_p$. The lower bound follows from a multilevel product principle applied to a scale-separated product of Euclidean simplices. The same construction gives the sharp convexification profile of $\ell_p^r(\ell_2^{2^{128r}})$ for $2
Source: arXiv (Cornell University)
Authors: Zhang, Helen W. J., Zhao, Chengdong
Institutions: Hunan University, Central South University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212002557