Taiwanese Journal of Mathematics

MAXIMAL REGULARITY FOR INTEGRO-DIFFERENTIAL EQUATION ON PERIODIC TRIEBEL-LIZORKIN SPACES

Shangquan Bu and Yi Fang

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Abstract

We study maximal regularity on Triebel-Lizorkin spaces $\mathrm{F} _{p,q}^s(\mathbb T, X)$ for the integro-differential equation with infinite delay: ($P_2$): $u'(t)=Au(t)+\int^{t}_{-\infty}a(t-s)Au(s)ds + f(t), \ (0\leq t \leq2\pi$) with the periodic condition $u(0)=u(2\pi)$, where $X$ is a Banach space, $a\in {\mathrm L}^1(\mathbb R_+)$ and $f$ is an $X$-valued function. Under a suitable assumption (H3) on the Laplace transform of $a$, we give a necessary and sufficient condition for ($P_2$) to have the maximal regularity property on $\mathrm{F} _{p,q}^s(\mathbb T, X)$.

Article information

Source
Taiwanese J. Math., Volume 12, Number 2 (2008), 281-292.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500574153

Digital Object Identifier
doi:10.11650/twjm/1500574153

Mathematical Reviews number (MathSciNet)
MR2402114

Zentralblatt MATH identifier
1151.45007

Subjects
Primary: 45N05: Abstract integral equations, integral equations in abstract spaces
Secondary: 45D05: Volterra integral equations [See also 34A12] 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 47D99: None of the above, but in this section

Keywords
integro-differential equation maximal regularity Triebel-Lizorkin spaces Fourier multiplier

Citation

Bu, Shangquan; Fang, Yi. MAXIMAL REGULARITY FOR INTEGRO-DIFFERENTIAL EQUATION ON PERIODIC TRIEBEL-LIZORKIN SPACES. Taiwanese J. Math. 12 (2008), no. 2, 281--292. doi:10.11650/twjm/1500574153. https://projecteuclid.org/euclid.twjm/1500574153


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