Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 1999; 36(1): 171-181

Printed March 1, 1999

Copyright © The Korean Mathematical Society.

The Volterra-Stieltjes integral equation and the operator-valued function space integral as an $\mathcal L(L_p, L_{p'})$ theory

Kun-Sik Ryu

Han Nam University

Abstract

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In this note, we will prove that the operator-valued function space integral as an operator from $L_p$ to $L_{p'} \ ( 1< p < 2 )$ for certain potential functionals satisfies a Volterra- Stieltjes integral equation.

Keywords: operator-valued function space integral, Volterra-Stieltjes integral equation

MSC numbers: 28C20

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