Spectral properties of the operator of Bessel potential type

Let Ω be a convex bounded domain in R m having regular boundary. In this paper, we study integral operators B m α on L 2 ( Ω ) of Bessel potential type. If N ( λ ) denotes the number of eigenvalues of B m α that are ≥λ, for λ > 0 , we find the asymptotics of the regularized eigenvalue distribution function λ ↦ ∫ λ ∞ N ( μ ) d μ when λ → 0 + . As a consequence, we find the regularized traces of these operators.