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Hytönen, Tuomas; Lappas, Stefanos

Quantitative estimates for bounded holomorphic semigroups. (English) Zbl 07825705

Semigroup Forum 108, No. 1, 115-144 (2024).
The authors of the paper under review revisit the theory of one-parameter semigroups of linear operators on Banach spaces in order to prove quantitative bounds for bounded holomorphic semigroups. In particular, they obtain new quantitative versions of two recent results of Xu related to the vector-valued Littlewood-Paley-Stein theory for symmetric diffusion semigroups. Moreover, the authors alsoquantify the dependence of the analyticity bounds for extensions of diffusion semigroups \((T(t))_{t\geq0}\) to uniformly convex spaces. Especially, they provide an explicit dependence of \(\sup_{t>0}\|t\partial T(t)\|\)s on the martingale cotype constant.
Reviewer: Christian Budde (Bloemfontein)

MSC:

47D03 Groups and semigroups of linear operators
47D07 Markov semigroups and applications to diffusion processes
42B25 Maximal functions, Littlewood-Paley theory

Keywords:

bounded holomorphic semigroups; symmetric diffusion semigroups; uniform convexity; martingale cotype; Littlewood-Paley-Stein theory
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