Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 2, Pages 161-164

Weighted norms and Volterra integral equations in LP spaces

Jaroslaw Kwapisz

Institute of Mathematics, Warsaw University, PKiN, Warsaw 00-901, Poland

Received 1 June 1990; Revised 1 October 1990

Copyright © 1991 Jaroslaw Kwapisz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new simple proof of existence and uniqueness of solutions of the Volterra integral equation in Lebesque spaces is given. It is shown that the weighted norm technique and the Banach contraction mapping principle can be applied (as in the case of continuous functions space).