A remark on the abstract Cauchy problem on spaces of Hölder continuous functions

Hieber, Matthias; Räbiger, Frank

doi:10.1090/S0002-9939-1992-1092921-X

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A remark on the abstract Cauchy problem on spaces of Hölder continuous functions

Authors: Matthias Hieber and Frank Räbiger
Journal: Proc. Amer. Math. Soc. 115 (1992), 431-434
MSC: Primary 47D03; Secondary 34G10, 47D06
MathSciNet review: 1092921
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the generator of a ${C_0}$ -semigroup on ${C^\alpha }({\mathbb{R}^n})$ is a bounded operator. Nevertheless, certain elliptic differential operators generate $\beta$ -times integrated semigroups on ${C^\alpha }({\mathbb{R}^n})$ whenever $\beta > n/2 + 1$ .

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