Analyticity and Discrete Maximal Regularity on Lp-Spaces☆

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H^\infty functional calculus and square function estimates for Ritt operators (2012, background): “We refer to [44], [46] for this characterization and also to [47], which contains the key argument, and to [7], [8] and Section 2 of [39] for complementary information.”
Power‐Bounded Operators and Related Norm Estimates (2002, background): “Let us finish this introduction by noting that Blunck [5], [6] gives many applications of the condition supn n‖T n+1 − T n‖ ∞ to maximal regularity problems.”
Weighted norm estimates and maximal regularity (2002, background): “This result is due Coulhon/Duong [10] who improved a weaker result due to Hieber/Prüss [17] ; see [5] for a short proof.”
Strong q-variation inequalities for analytic semigroups (2011, background): “We gather here a few spectral properties of these operators and refer to [3, 22, 24, 25] for proofs and complements.”