Abstract
We revisit the theory of one-parameter semigroups of linear operators on Banach spaces in order to prove quantitative bounds for bounded holomorphic semigroups. Subsequently, relying on these bounds we obtain new quantitative versions of two recent results of Xu related to the vector-valued Littlewood–Paley–Stein theory for symmetric diffusion semigroups.
| Original language | English |
|---|---|
| Pages (from-to) | 115-144 |
| Number of pages | 30 |
| Journal | Semigroup Forum |
| Volume | 108 |
| Issue number | 1 |
| Early online date | 2024 |
| DOIs | |
| Publication status | Published - Feb 2024 |
| MoE publication type | A1 Journal article-refereed |
Funding
Both authors were supported by the Academy of Finland through project Nos. 314829 (“Frontiers of singular integrals”) and 346314 (“Finnish Centre of Excellence in Randomness and Structures”). Also, the second author would like to thank the Foundation for Education and European Culture (Founders Nicos and Lydia Tricha), Greece, for their financial support. We would like to thank the anonymous referee for careful reading and constructive comments that improved the presentation.
Keywords
- Bounded holomorphic semigroups
- Littlewood–Paley–Stein theory
- Martingale cotype
- Symmetric diffusion semigroups
- Uniform convexity
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