The operator-valued Marcinkiewicz multiplier theorem and maximal regularity
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Given a closed linear operator on a UMD-space, we characterize maximal regularity of the non-homogeneous problem
$u' + Au = f$
with periodic boundary conditions in terms of R-boundedness of the resolvent. Here A is not necessarily generator of a $C_0$ -semigroup. As main tool we prove an operator-valued discrete multiplier theorem. We also characterize maximal regularity of the second order problem for periodic, Dirichlet and Neumann boundary conditions.
- The operator-valued Marcinkiewicz multiplier theorem and maximal regularity
Volume 240, Issue 2 , pp 311-343
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