School of Science
Hubei University of Technology
Wuhan 430068, China
email: 156880717@qq.com
Department of Mathematical Science
Tsinghua University
Beijing 100084, China
email: bushangquan@tsinghua.edu.cn
Jichao Zhang, Shangquan Bu
Abstract:
In this article, we study the \(\ell^p\)-maximal regularity for the fractional
difference equation
$$
\Delta^{\alpha}u(n)=Tu(n)+f(n), \quad (n\in \mathbb{N}_0).
$$
We introduce the notion of \(\alpha\)-resolvent sequence of bounded linear operators
defined by the parameters \(T\) and \(\alpha\), which gives an explicit representation
of the solution. Using Blunck's operator-valued Fourier multipliers theorems on
\(\ell^p(\mathbb{Z}; X)\), we give a characterization of the \(\ell^p\)-maximal regularity
for \(1 < p < \infty\) and \(X\) is a UMD space.
Submitted March 12, 2023. Published February 26, 2024.
Math Subject Classifications: 47A10, 35R11, 35R20, 43A22.
Key Words: Fractional difference equation; maximal regularity; UMD space; R-bounded.
DOI: 10.58997/ejde.2024.20
Show me the PDF file (378 KB), TEX file for this article.
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Jichao Zhang School of Science Hubei University of Technology Wuhan 430068, China email: 156880717@qq.com |
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Shangquan Bu Department of Mathematical Science Tsinghua University Beijing 100084, China email: bushangquan@tsinghua.edu.cn |
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