For the solution to u(x, t) – Δu(x, t) + q(x)u(x, t) = δ(x ₁)δ′´(t) and u|_t<0 = 0, we consider an inverse problem of determining q(x), x ∈ Ω from data ƒ = u|_ST and g = (∂u/∂v)|_ST. Here Ω ⊂ {(x ₁, . . . , x _n) ∈ |x ₁ > 0}, n ≥ 2, is a bounded domain, S _T = {(x, t) | x ∈ ∂Ω, x ₁ < t < T + x ₁} and T > 0. For suitable T > 0, we prove an L ² (Ω)-size estimation of q:

||q||L ²(Ω) ≤ C{||ƒ||H ¹(S _T) + ||g||L ²(S_T)},

provided that q satisfies a priori uniform boundedness conditions. We use an inequality of Carleman type in our proof.