Fractional Integration and Fractional Differentiation for d-dimensional Jacobi Expansions

2006/08/25 by Cristina Balderrama, Balderrama, Cristina, Wilfredo Urbina +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 42C10 #Secondary 26B99 #Thermoelastic and Magnetoelastic Phenomena #math.AP #msc:26B99 #msc:42C10

paper · pdf · doi:10.48550/arxiv.math/0608639

23 pages; V2 Minor changes. Corrected Typos

openalex publication_date 2006/08/25 · arxiv created 2007/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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