TY - JOUR AU - K. V. Shvai PY - 2018/04/25 Y2 - 2024/03/28 TI - Estimates of the best bilinear approximations for the classes of $(ψ,β)$-differentiable periodic multivariate functions JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 70 IS - 4 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1576 AB - Order estimates are obtained for the best bilinear approximations of $2d$-variable functions $f(x y),\;x, y \in \pi_d,\; \pi_d =\prod^d_{j=1} [ \pi , \pi ]$, formed by $d$-variable functions $f(x) \in L^{\psi}_{\beta} ,p$ by the shifts of their argument $x \in \pi_d$ by all possiblevalues of $y \in \pi_d$ in the space $L_{q_1,q_2} (\pi 2d)$. The results include various relations between the parameters $p, q_1$ and $q_2$. ER -