A Cohen-type Inequality For Jacobi-sobolev Expansions

摘要

Let μ be the Jacobi measure supported on the interval [ -1, 1]. Let us introduce the Sobolev-type inner product (f,g) = ∫_(-1)~1f(x)g(x)dμ(x)+Mf(1)g(1) + Nf'(1)g'(1), where M,N ≥ 0. In this paper we prove a Cohen-type inequality for the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product. We follow Dreseler and Soardi (1982) and Markett (1983) papers, where such inequalities were proved for classical orthogonal expansions.