A transference principle for general groups and functional calculus on UMD spaces
A transference principle for general groups and functional calculus on UMD spaces
Let –iA be the generator of a C 0-group $${(U(s))_{s\in \mathbb {R}}}$$ on a Banach space X and ω > θ(U), the group type of U. We prove a transference principle that allows to estimate $${||{f(A)}||}$$ in terms of the $${{\rm{L}}^{p}(\mathbb {R};X)}$$ -Fourier multiplier norm of $${f(\cdot \pm i \omega)}$$ …