Let
N be an integral operator of the form
acting in
Lp(Rc) with a measurable kernel
n satisfying the estimate
where
β∈L1. It is proved that if the function
b5589e13d0c15e56fe71f606f" title="Click to view the MathML source">t↦n(t,⋅) is continuous in the norm of
93bb3f68546ef93bbd4716eb3de" title="Click to view the MathML source">L1 and the operator
1+N has an inverse, then
(1+N)−1=1+M, where
M is an integral operator possessing the same properties.