Hadamard's finite part concept in dimension n[ges ]2; definition and change of variables, associated Fubini's theorem, derivation

Abstract

Some usual and important operations: change of variables, application of Fubini's theorem and derivation with respect to the isolated singularity (in the present work with respect to the origin of the spherical coordinates (r, θ)) are studied for the following singular integral

formula here

where α∈C, Re(α)[les ]−n, j∈ℕ, α∈L¹([sum ]_n, C) and the symbol fp∫_{Ω, U} means an integration on the set Ω in the finite part sense of Hadamard with respect to the domain configuration U. Moreover, applications to integral operators are outlined.