抄録
Let f : Rn → R be a polynomial function of degree d with f(0) = 0. The classical Łojasiewiz inequality states that there exist c > 0 and α > 0 such that |f(x)| ≥ cd(x, f–1(0))α in a neighbourhod of the origin 0 ∈ Rn, where d(x, f–1 (0)) denotes the distance from x to the set f–1(0). We prove that the smallest such exponent α is not greater than R(n, d) with R(n, d) := max{d(3d – 4)n–1, 2d(3d – 3)n–2}.
