Functional calculus for generators of symmetric contraction semigroups. (English) Zbl 1476.47015

Carbonaro, Andrea; Dragičević, Oliver

Duke Math. J. 166, No. 5, 937-974 (2017).

Summary: We prove that every generator of a symmetric contraction semigroup on a \(\sigma\)-finite measure space admits, for \(1< p< \infty\), a Hörmander-type holomorphic functional calculus on \(L^{p}\) in the sector of angle \(\phi^{\ast}_{p}=\arcsin|1-2/p|\). The obtained angle is optimal.

MSC:

47A60	Functional calculus for linear operators
42B15	Multipliers for harmonic analysis in several variables
47D03	Groups and semigroups of linear operators
42B25	Maximal functions, Littlewood-Paley theory

Keywords:

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