Parts formulas involving integral transforms on function space
Commun. Korean Math. Soc. 2007 Vol. 22, No. 4, 553-564 Printed December 1, 2007
Bong Jin Kim, Byoung Soo Kim Daejin University, Seoul National University of Technology
Abstract : In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(\langle \theta_1,y\rangle,\ldots,\langle \theta_n,y\rangle)$ for s-a.e. $y\in C_0 [0, T]$, where $\langle\theta,y\rangle$ denotes the Riemann-Stieltjes integral $\int_0^T \theta(t)\,dy(t)$.
Keywords : integral transform, convolution product, first variation, integration by parts formula, Wiener integral