Quantitative estimates for bounded holomorphic semigroups
Abstract
In this paper 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.14198
- arXiv:
- arXiv:2208.14198
- Bibcode:
- 2022arXiv220814198H
- Keywords:
-
- Mathematics - Functional Analysis;
- Mathematics - Classical Analysis and ODEs;
- 47D03 (Primary);
- 42B25;
- 46B20
- E-Print:
- V3: 27 pages. Fixed several details in Section 5, also affecting the statement of Theorem 5.1. Eq. (5.2) now has B^{k+1} in place of the previous B^2 that resulted from oversights in the earlier versions. V2: 26 pages. Revised according to referee comments. To appear in Semigroup Forum. arXiv admin note: text overlap with arXiv:1803.05107 by other authors