We consider the equation

where

Under these conditions, (1) is correctly solvable in L1(ℝ), i.e.

(i) for any function f ∈ L1(ℝ), there exists a unique solution of (1), y ∈ L1(ℝ);

(ii) there is an absolute constant c1 ∈ (0, ∞) such that the solution of (1),

In this work we strengthen the a priori inequality (1). We find minimal requirements for a given weight function θ ∈ Lloc1(ℝ) under which the solution of (1), y ∈ L1(ℝ), satisfies the estimate

where c2 is some absolutely positive constant.