### 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 |
---|---|

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 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

^{p}-spaces via the transference principle.

*Advances in Differential Equations*,

*3*(6), 847-876.

**Functional calculi for linear operators in vector-valued L ^{p}-spaces via the transference principle.** / Hieber, Matthias Georg; Prüss, Jan.

Research output: Contribution to journal › Article

^{p}-spaces via the transference principle',

*Advances in Differential Equations*, vol. 3, no. 6, pp. 847-876.

}

TY - JOUR

T1 - Functional calculi for linear operators in vector-valued Lp-spaces via the transference principle

AU - Hieber, Matthias Georg

AU - Prüss, Jan

PY - 1998

Y1 - 1998

N2 - Let-A be the generator of a bounded C0-group or of a positive contraction semigroup, respectively, on Lp(ω,μ,Y), where (ω,μ)is measure space, Y is a Banach space of class HT and 1 ∞-calculus on each double cone Cθ = {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 Lp(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 Cθ, θ > 0, and that-A2 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.

AB - Let-A be the generator of a bounded C0-group or of a positive contraction semigroup, respectively, on Lp(ω,μ,Y), where (ω,μ)is measure space, Y is a Banach space of class HT and 1 ∞-calculus on each double cone Cθ = {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 Lp(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 Cθ, θ > 0, and that-A2 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.

UR - http://www.scopus.com/inward/record.url?scp=0242301439&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242301439&partnerID=8YFLogxK

M3 - Article

VL - 3

SP - 847

EP - 876

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 6

ER -