An integral transform associated to the Poisson integral and inversion of Flett potentials

We introduce a new weighted wavelet-like transform, generated by the Poisson integral and a “wavelet measure.” By making use of the relevant Calderón-type reproducing formula, we obtain an explicit inversion formula for the Flett potentials which are interpreted as negative fractional powers of the operator (E +Λ), where Λ = (−Δ)1/2, Δ is the Laplacian and E is the identity operator. © 2005 Elsevier Inc. All rights reserved