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

Research output: Contribution to journalArticle

35 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

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Functional Calculus
Banach spaces
Lp Spaces
Linear Operator
Calculus
Sector
Banach space
Generator
Positive Semigroup
Contraction Semigroup
Measure space
Elliptic Boundary Value Problems
Boundary value problems
Cones
Cone
Class

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Functional calculi for linear operators in vector-valued Lp-spaces via the transference principle. / Hieber, Matthias Georg; Prüss, Jan.

In: Advances in Differential Equations, Vol. 3, No. 6, 1998, p. 847-876.

Research output: Contribution to journalArticle

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