The convergence of multidimensional Fourier-Bessel series
The Dirichlet problem for the unit ball in the \(d\)-dimensional space is considered in \(L^p_{\text{rad}}(L^2_{\text{ang}})\). For \(2d/(d+ 1)< p< 2d/(d- 1)\) a convergence result for eigenfunction expansions is obtained. There is some connection with the spherical summation of trigonometric expansions. Tools are van der Corput estimates for decompositions of oscillatory integrals, and inequalities for weighted singular integrals.
scientific article; zbMATH DE number 1309906