Harmonic analysis and integral transforms associated with a class of a system of partial differential operators

In this work, we consider a generalized system of partial differential operators, we define the related Fourier transform and establish some harmonic analysis results. We also investigate a wide class of integral transforms of Riemann-Liouville type. In particular we give a good estimate of these integrals kernels, inversion formula and a Plancherel theorem for the dual.