In this paper we consider an alternative orthogonal decomposition of the space L 2 associated to the d-dimensional Jacobi measure in order to 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 Sobolev or potential spaces and a version of Calderón's reproduction formula for the d-dimensional Jacobi measure. R ÉSUM É. Dans cet article nous considérons une décomposition orthogonale alternative de l'espace L 2 associée à la mesure de Jacobi d-dimensionelle afin d'obtenir de résultat analogues au Théorème des Multiplicateurs de P.A. Meyer pour les développements d-dimensionnels de Jacobi. Nous définissons et étudions l'integral Fractionnaire, la dérivée Fractionnaire et les potentiels de Bessel induits par l'operateur de Jacobi. Nous obtenons ègalement une charactérisation des espaces
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