  In this paper we consider an alternative orthogonal decomposition of the
space $L^2$ associated to the $d$-dimensional Jacobi measure and obtain an
analogous result to P.A. Meyer's Multipliers Theorem for d-dimensional Jacobi
expansions. Then we define and study the Fractional Integral, the Fractional
Derivative and the Bessel potentials induced by the Jacobi operator. We also
obtain a characterization of the potential spaces and a version of Calderon's
reproduction formula for the d-dimensional Jacobi measure.
