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

Matthias Georg Hieber, Jan Prüss

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)847-876
Number of pages30
JournalAdvances in Differential Equations
Volume3
Issue number6
Publication statusPublished - 1998
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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