Estimates of the Lebesgue function of Fourier sums in trigonometric polynomials orthogonal with a weight not belonging to the spaces L (r) (r > 1)

Abstract

A two-sided pointwise estimate is obtained for the Lebesgue function of Fourier sums in trigonometric polynomials orthogonal with a 2π-periodic weight that differs from the function 1/{pipe} sin(τ/2){pipe} by some factor slowly changing at zero. The weight under consideration does not belong to the space L r for any r > 1. A similar result for polynomials orthogonal on the interval [-1, 1] is obtained in the form of a corollary. © 2012 Pleiades Publishing, Ltd.