On multipliers for Fourier series in Sobolev orthogonal polynomials

Abstract

Multipliers are studied for Fourier series in polynomials orthogonal in continuous-discrete Sobolev spaces. For the multiplier operator, existence results and norm estimates are obtained. The proofs are based on a representation of the Fejér kernel, the construction of a ‘humpbacked majorant’ and estimates for the norms of maximal functions. Bibliography: 45 titles.