Fourier-Laplace transforms and related questions on certain analytic varieties in C2

For an analytic variety Vφ={(z1,z2)∈C2:φ(z1,z2)=0}, defined by a holomorphic function φ, we assume that the point 0∈Vφ and that Vφ−{0} is smooth. In this setting, we construct holomorphic differentials θ, on Vφ−{0}, with prescribed certain of the values of the integrals ∫z1kz2lθ(z1,z2), taken over closed curves on Vφ which surround 0. The construction is quite explicit and is based on a residue process. We also study similar questions with specific choices of φ, in which cases we obtain more complete results.