Abstract.
We establish a transference result for \(L^p\)-maximal regularity for the abstract Cauchy problem on Banach space. From this result we deduce counterexamples to \(L^p\)-maximal regularity \((1 < p < \infty).\) In particular we obtain an operator B without any \(L^p\)-maximal regularity although it admits bounded imaginary powers with \(\Vert B^{is}\Vert = 1\) for all \(s \in \mathbb{R}\). We also derive an operator which satisfies \(L^p\)-maximal regularity on bounded intervals [0, T[ but not on the half line \(\mathbb{R}_{+}.\)
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Received March 5, 1997; in final form October 10, 1997
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Le Merdy, C. Counterexamples on \(L_p\)-maximal regularity. Math Z 230, 47–62 (1999). https://doi.org/10.1007/PL00004688
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DOI: https://doi.org/10.1007/PL00004688