A refinement of Baillon’s theorem on maximal regularity
Volume 263 / 2022
Studia Mathematica 263 (2022), 141-158
MSC: Primary 47D06, 35K90; Secondary 47B37.
DOI: 10.4064/sm200731-20-3
Published online: 31 January 2022
Abstract
By Baillon’s theorem, it is known that maximal regularity with respect to the space of continuous functions is rare; it implies that either the semigroup generator involved is a bounded operator or the space considered contains $c_{0}$. We show that the latter alternative can be excluded under a refined condition resembling maximal regularity with respect to $\mathrm {L}^{\infty }$.
