Divergent Cesàro Means of Jacobi-Sobolev Expansions

Abstract

Let μ be the Jacobi measure supported on the interval [−1, 1]. Let introduce the Sobolev-type inner productwhere M, N ≥ 0. In this paper we prove that, for certain indices δ, there are functions whose Cesàro means of order δ in the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product are divergent almost everywhere on [−1, 1].