# A Besov algebra calculus for generators of operator semigroups and related norm-estimates

Batty, C
Gomilko, A
Tomilov, Y

1 January 2019

## Journal:

Mathematische Annalen

## Last Updated:

2020-06-13T22:07:19.423+01:00

1

## DOI:

10.1007/s00208-019-01924-2

1-66

## abstract:

© 2019, The Author(s). We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical Hille–Phillips functional calculus, and it is compatible with the other well-known functional calculi. It satisfies the standard properties of functional calculi, provides a unified and direct approach to a number of norm-estimates in the literature, and allows improvements of some of them.

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