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Bounded H ∞ ‐calculus for pseudo‐differential Douglis–Nirenberg systems of mild regularity
Author(s) -
Denk Robert,
Saal Jürgen,
Seiler Jörg
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810743
Subject(s) - mathematics , bounded function , nirenberg and matthaei experiment , sobolev space , pure mathematics , class (philosophy) , mathematical analysis , thermoelastic damping , differential equation , differential (mechanical device) , calculus (dental) , thermodynamics , physics , dentistry , thermal , medicine , artificial intelligence , computer science
We consider pseudo‐differential Douglis–Nirenberg systems on ℝ n with components belonging to the standard Hörmander class S 1, δ * (ℝ n × R n ), 0 ≤ δ < 1. Parameter‐ellipticity with respect to a subsector Λ ⊂ ℂ is introduced and shown to imply the existence of a bounded H ∞ ‐calculus in suitable scales of Sobolev, Besov, and Hölder spaces. We also admit non pseudo‐differential perturbations. Applications concern systems with coefficients of mild Hölder regularity and the generalized thermoelastic plate equations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)