## Differential and Integral Equations

### A Stieltjes type convolution for integrated semigroups of bounded strong variation and $L_p$-solutions to the abstract Cauchy problem

#### Abstract

A convolution of Stieltjes type is introduced for operator families of bounded strong variation and vector valued $L_1$-functions. Using this tool, perturbation theorems for integrated semigroups of bounded strong variation are derived, and improved results on $L_p$-solutions to the inhomogeneous Cauchy problem are obtained.

#### Article information

Source
Differential Integral Equations, Volume 15, Number 10 (2002), 1171-1218.

Dates
First available in Project Euclid: 21 December 2012

Thieme, Horst R.; Vosseler, Hauke. A Stieltjes type convolution for integrated semigroups of bounded strong variation and $L_p$-solutions to the abstract Cauchy problem. Differential Integral Equations 15 (2002), no. 10, 1171--1218. https://projecteuclid.org/euclid.die/1356060751