bibkey: llinares2021contractive
authors: A. Llinares and D. Vukotić
year: 2022
title: "Contractive inequalities for mixed norm spaces and the Beta function"
doi: null
url: https://arxiv.org/abs/2107.05542
claim: "Contractive inclusions of mixed norm spaces are characterized for p at least u; the point-evaluation problem has p below u equal to infinity."
strata_touched:
  - D5/S3/Analytic/MixedNorm/DmitrovicPointEvaluation/Result
license: citation-only
triage: anchor

Contractive mixed-norm inclusions

Locator

Author text: https://arxiv.org/abs/2107.05542

A. Llinares and D. Vukotić, Contractive inequalities for mixed norm spaces and the Beta function, Journal of Mathematical Analysis and Applications 509 (2022), 125938; arXiv:2107.05542.

Source statement

The paper characterizes contractive inclusions $H(p,q,a)\subset H(u,v,b)$ under the hypothesis $p\ge u$. It describes the complementary range $p<u$ as very difficult.

The constant-one point-evaluation conjecture corresponds to the contractive inclusion $H(p,q,\alpha )\subset H(\infty ,\infty ,\alpha +1/p)$. For finite p this has $p<u=\infty$, outside the characterized range.

Source boundary

This reference supplies context, not the refutation or a theorem imported by the Lean development. Its arXiv URL is the bound locator. A journal DOI is not asserted because no arXiv metadata confirming it is available in the local source material. The exact point-evaluation norm for q greater than p remains undetermined here.