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- W200112750 abstract "Heat kernel estimates play an important role in the investigation of the question whether or not a given sectorial operator admits bounded imaginary powers or an H∞-calculus on an L p space. Indeed, it was shown in [7] and [10] that, roughly speaking, the negative of a given generator —A of a holomorphic semigroup T on L 2(Ω) admits an H ∞-calculus on L p (Ω), 1 < p < ∞, with optimal angle, provided the following conditions hold: A admits an H ∞-calculus on L 2 (Ω), the operators T(t) are integral operator for all t > 0 and Ω as well as the kernel of T (t) or the kernel of the resolvent of —A satisfy certain regularity conditions. These conditions are in particular satisfied whenever Ω is a bounded Lipschitz domain in ℝ n , (n ≥ 3), T satisfies an upper Gaussian estimate and the kernel of the resolvent of —A satisfies a certain Hölder regularity assumption." @default.
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- W200112750 date "1995-01-01" @default.
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- W200112750 title "H∞-Calculus for Second Order Elliptic Operators in Divergence Form" @default.
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- W200112750 doi "https://doi.org/10.1007/978-3-0348-9092-2_20" @default.
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