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The analysis of the dependence of integral operators on perturbations playsan important role in the study of inverse problems and of perturbed boundaryvalue problems. In this paper we focus on the mapping properties of the volumepotentials with weakly singular periodic kernels. Our main result is to provethat the map which takes a density function and a periodic kernel to a(suitable restriction of the) volume potential is bilinear and continuous withvalues in a Roumieu class of analytic functions. Such result extends to theperiodic case some previous results obtained by the authors for non periodicpotentials and it is motivated by the study of perturbation problems for thesolutions of boundary value problems for elliptic differential equations inperiodic domains.

Mapping properties of weakly singular periodic volume potentials in Roumieu classes