Duke Mathematical Journal

Functional calculus for generators of symmetric contraction semigroups

Andrea Carbonaro and Oliver Dragičević

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We prove that every generator of a symmetric contraction semigroup on a σ-finite measure space admits, for 1<p<, a Hörmander-type holomorphic functional calculus on Lp in the sector of angle ϕp=arcsin|12/p|. The obtained angle is optimal.

Article information

Duke Math. J., Volume 166, Number 5 (2017), 937-974.

Received: 10 August 2015
Revised: 9 June 2016
First available in Project Euclid: 20 December 2016

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Zentralblatt MATH identifier

Primary: 47A60: Functional calculus 42B15: Multipliers 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}
Secondary: 42B25: Maximal functions, Littlewood-Paley theory

functional calculus spectral multipliers symmetric contraction semigroups Bellman functions maximal functions Littlewood–Paley theory


Carbonaro, Andrea; Dragičević, Oliver. Functional calculus for generators of symmetric contraction semigroups. Duke Math. J. 166 (2017), no. 5, 937--974. doi:10.1215/00127094-3774526. https://projecteuclid.org/euclid.dmj/1482202830

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