Lebesgue inequalities for poisson integrals

• Date: 2000
• Main Authors: Serdyuk, A. S., Stepanets, O. I., Сердюк, А. С., Степанец, А. И.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4474
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the spaceL p ,p≥1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric ofL p . We show that the es...