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 The Volterra-Stieltjes integral equation and the operator-valued function space integral as an $\mathcal L(L_p, L_{p'})$ theory Bull. Korean Math. Soc. 1999 Vol. 36, No. 1, 171-181 Kun-Sik Ryu Han Nam University Abstract : 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 Downloads: Full-text PDF