Spectral properties of the operator of Bessel potential type

Let Ω be a convex bounded domain in Rm having regular boundary. In this paper, we study integral operators Bmα on L2(Ω) of Bessel potential type. If N(λ) denotes the number of eigenvalues of Bmα that are ≥λ, for λ>0, we find the asymptotics of the regularized eigenvalue distribution function λ↦∫λ∞N(μ)dμ when λ→0+. As a consequence, we find the regularized traces of these operators.