An integral operator related to the Stokes system in exterior domains

Consider a bounded domain Ω in ℝ 3 with C 2 ‐boundary ∂Ω. In [1] the Stokes problem in the exterior domain ℝ 3 / Ω , with resolvent parameter [λϵℂ\] − [∞,0], is solved by using the method of integral equations. However, for estimating the corresponding solutions in L p norms, it turns out that a certain operator defined on the spaces L r (∂Ω) 3 , for r ϵ]1, ∞[, has to be evaluated in the norm of L r (∂Ω) 3 . This estimate is proved in the present paper.