Let

$B(a) = \left\{ {x \in IR^3 /\left| x \right| \leqslant a} \right\},a > 0.$B(a) = \left\{ {x \in IR^3 /\left| x \right| \leqslant a} \right\},a > 0.

The main aim of the paper is to solve the integral equation:

g(x) = òB(a) f(x + y)dy, x Î IR3 ,g(x) = \int_{B(a)} {f(x + y)dy, x \in IR^3 ,}

for a given functiong. Following the ideas of F. John [1] and [2] we show that from a plane-wave decomposition ofg, one can explicitly construct a solution. We also give conditions ong such that a unique solution exists and analyse the case wheng ∈D(IR)³ — the space theC ^∞-functions on IR³ with compact support.