An integral transform associated to the Poisson integral and inversion of flett potentials (Q2496690)

The authors introduce continuous wavelet transforms generated by fractional powers of the operator \(I+\Lambda\), where \(\Lambda= (-\Delta)^{1/2}\), \(\Delta\) is the Laplacian in \(\mathbb{R}^n\). An analogue of the Calderón reproducing formula and inversion formulas for Flett potentials, realizing negative powers of \(I+\Lambda\), are obtained in the framework of the \(L^p\)-theory.