# A Besov class functional calculus for bounded holomorphic semigroups

@inproceedings{Vitse2005ABC, title={A Besov class functional calculus for bounded holomorphic semigroups}, author={Pascale Vitse}, year={2005} }

- Published 2005
DOI:10.1016/j.jfa.2005.01.010

Abstract It is well-known that π 2 -sectorial operators generally do not admit a bounded H ∞ calculus over the right half-plane. In contrast to this, we prove that the H ∞ calculus is bounded over any class of functions whose Fourier spectrum is contained in some interval [ e , σ ] with 0 e σ ∞ . The constant bounding this calculus grows as log σ e e as σ e → ∞ and this growth is sharp over all Banach space operators of the class under consideration. It follows from these estimates that π 2… CONTINUE READING

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