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20 April 2024

» arxiv » 1411.4240

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Maximal Regularity: Positive Counterexamples on UMD-Banach Lattices and Exact Intervals for the Negative Solution of the Extrapolation Problem
Stephan Fackler ;
Date:	16 Nov 2014
Abstract:	Using methods from Banach space theory, we prove two new structural results on maximal regularity. The first says that there exist positive analytic semigroups on UMD-Banach lattices, namely $ell_p(ell_q)$ for $p eq q in (1, infty)$, without maximal regularity. In the second result we show that the extrapolation problem for maximal regularity behaves in the worst possible way: for every interval $I subset (1, infty)$ with $2 in I$ there exists a family of consistent bounded analytic semigroups $(T_p(z))_{z in Sigma_{pi/2}}$ on $L_p(mathbb{R})$ such that $(T_p(z))$ has maximal regularity if and only if $p in I$.
Source:	arXiv, 1411.4240
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