### Abstract

Let-A be the generator of a bounded C_{0}-group or of a positive contraction semigroup, respectively, on L^{p}(ω,μ,Y), where (ω,μ)is measure space, Y is a Banach space of class HT and 1 <p <∞. If Y = ℂ ℂ, it is shown by means of the transference principle due to Coifman and Weiss that A admits an H^{∞}-calculus on each double cone C_{θ} = {λ ε ℂ\{0} : | arg λ ± π/2| <θ}, where θ > 0 and on each sector ∑_{θ} = {λ ε ℂ\{0} : | arg λ| <θ} with θ > π/2, respectively. Several extensions of these results to the vector-valued case L^{p}(ω,μ,Y) are presented. In particular, let-A be the generator of a bounded group on a Banach spaces of class HT. Then it is shown that A admits an H_{∞}-calculus on each double cone C_{θ}, θ > 0, and that-A_{2} admits an H_{∞}-calculus on each sector ∑_{θ};, where θ > 0. Applications of these results deal with elliptic boundary value problems on cylindrical domains and on domains with non smooth boundary.

Original language | English |
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Pages (from-to) | 847-876 |

Number of pages | 30 |

Journal | Advances in Differential Equations |

Volume | 3 |

Issue number | 6 |

Publication status | Published - 1998 |

Externally published | Yes |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

^{p}-spaces via the transference principle.

*Advances in Differential Equations*,

*3*(6), 847-876.