TY - JOUR
AU - A. S. Serdyuk
PY - 2005/10/25
Y2 - 2024/11/14
TI - Approximation of classes of analytic functions by Fourier sums in the metric of the space $L_p$
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 57
IS - 10
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3693
AB - 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.
ER -