Differential and Integral Equations

Integral operators in spaces of bounded, almost periodic, and almost automorphic functions

Gaston M. N'Guérékata and Alexander Pankov

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Abstract

In this paper we consider integral operators on the real line and derive certain sufficient conditions under which the operators act as bounded linear operators between the spaces of Stepanov bounded functions. Next, we find conditions that insure the operators act between spaces of Stepanov almost periodic, or between spaces of Stepanov almost automorphic, functions. We apply these results to ordinary differential equations and obtain the existence and uniqueness of bounded, almost periodic, and almost automorphic solutions.

Article information

Source
Differential Integral Equations, Volume 21, Number 11-12 (2008), 1155-1176.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1355502297

Mathematical Reviews number (MathSciNet)
MR2482500

Zentralblatt MATH identifier
1224.45021

Subjects
Primary: 47B38: Operators on function spaces (general)
Secondary: 34C27: Almost and pseudo-almost periodic solutions 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 45P05: Integral operators [See also 47B38, 47G10] 47G10: Integral operators [See also 45P05]

Citation

N'Guérékata, Gaston M.; Pankov, Alexander. Integral operators in spaces of bounded, almost periodic, and almost automorphic functions. Differential Integral Equations 21 (2008), no. 11-12, 1155--1176. https://projecteuclid.org/euclid.die/1355502297


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