缓变分数阶Cauchy问题解的极大正则性

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-09-17 DOI:10.1016/j.jfa.2025.111196

Edgardo Alvarez , Carlos Lizama , Marina Murillo-Arcila

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引用次数: 0

摘要

设X是巴拿赫空间。给定一个定义在X上的闭线性算子a，我们证明了在向量值Hölder空间Cα(R，X)（0<α<1）中，当我们给柯西问题赋予缓变分数阶导数时，抽象柯西问题的最大正则性可以仅用算子a的谱性质来表征。特别地，我们证明了有界解析半群的生成子具有极大正则性。

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Maximal regularity of solutions for the tempered fractional Cauchy problem

Let X be a Banach space. Given a closed linear operator A defined on X we show that, in vector-valued Hölder spaces

C^{α} (R, X) (0 < α < 1)

, maximal regularity for the abstract Cauchy problem can be characterized solely in terms of a spectral property of the operator A, when we equip the Cauchy problem with the tempered fractional derivative. In particular, we show that generators of bounded analytic semigroups admit maximal regularity.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis