Approximation of classes of analytic functions by Fourier sums in the metric of the space $L_p$

  • A. S. Serdyuk


Asymptotic equalities are established for upper bounds of approximants by Fourier partial sums in a metric of spaces $L_p,\quad 1 \leq p \leq \infty$ on classes of the Poisson integrals of periodic functions belonging to the unit ball of the space $L_1$. The results obtained are generalized to the classes of $(\psi, \overline{\beta})$-differentiable functions (in the Stepanets sense) that admit the analytical extension to a fixed strip of the complex plane.
How to Cite
Serdyuk, A. S. “Approximation of Classes of Analytic Functions by Fourier Sums in the Metric of the Space $L_p$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 10, Oct. 2005, pp. 1395–1408,
Research articles