Fractional Integration and Fractional Differentiation for d-dimensional Jacobi Expansions
Cristina Balderrama, Wilfredo Urbina
Abstract
In this paper we consider an alternative orthogonal decomposition of the space L2 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.
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