Abstract
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.
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