抄録
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 <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 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.
本文言語 | English |
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ページ(範囲) | 847-876 |
ページ数 | 30 |
ジャーナル | Advances in Differential Equations |
巻 | 3 |
号 | 6 |
出版ステータス | Published - 1998 |
外部発表 | はい |
ASJC Scopus subject areas
- 分析
- 応用数学