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Archiv der Mathematik

, Volume 82, Issue 5, pp 415–431 | Cite as

Maximal regularity for evolution equations in weighted L p -spaces

  • J. PrüssEmail author
  • G. SimonettEmail author
Original paper

Abstract.

Let X be a Banach space and let A be a closed linear operator on X. It is shown that the abstract Cauchy problem

\( \dot{u}(t) + Au(t) = f(t),\; t > 0,\quad u(0) = 0, \)

enjoys maximal regularity in weighted L p -spaces with weights \( \omega(t) = t^{p(1-\mu)} \), where \( 1/p < \mu \), if and only if it has the property of maximal L p -regularity. Moreover, it is also shown that the derivation operator \( D = d/dt \) admits an \( {\cal H}^\infty \)-calculus in weighted L p -spaces.

Mathematics Subject Classification (2000):

35K90 47A60 35K55. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Fachbereich Mathematik und InformatikMartin-Luther-Universität Halle-WittenbergHalleGermany
  2. 2.Department of MathematicsVanderbilt UniversityNashvilleUSA

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