A Cohen type inequality for Fourier expansions of orthogonal polynomials with a non‐discrete Gegenbauer‐Sobolev inner product

Abstract

Let dμ(x) = (1 − x2)α−1/2dx,α> − 1/2, be the Gegenbauer measure on the interval [ − 1, 1] and introduce the non‐discrete Sobolev inner product where λ>0. In this paper we will prove a Cohen type inequality for Fourier expansions in terms of the polynomials orthogonal with respect to the above inner product. Results on divergence for Cesàro means of Gegenbauer‐Sobolev expansions are deduced. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim