Novel interpolation spaces and maximal‐weighted Hölder regularity results for the fractional abstract Cauchy problem

Yuting Chen and Zhenbin Fan

Mathematische Nachrichten, 2024, vol. 297, issue 2, 560-576

Abstract: In this paper, the maximal‐weighted Hölder regularity for the fractional abstract Cauchy problem is presented. First, two classes of novel interpolation spaces constructed by resolvent families are portrayed. Afterward, by applying the resolvent method and the properties of interpolation spaces, the maximal‐weighted Hölder regularity of the mild solution is established in weighted Hölder space C0β,γ(X)$C_0^{\beta ,\gamma }(X)$ (0≤γ≤β$0\le \gamma \le \beta$, 0

Date: 2024
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https://doi.org/10.1002/mana.202300093

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:297:y:2024:i:2:p:560-576

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