Linear and Kolmogorov Widths of the Classes $$ {B}_{p,\uptheta}^{\Omega} $$ of Periodic Functions of One and Several Variables

Abstract

Abstract. Some estimates exact in order for linear widths of the classes $$ {B}_{p,\uptheta}^{\Omega} $$ of periodic multivariable functions in the space Lq with certain relations between the parameters p, q; and 𝜃 are obtained. In the univariate case, the estimates exact in order for Kolmogorov and linear widths of the classes $$ {B}_{\infty, \uptheta}^{\omega } $$ in the space Lq, 1 ≤ q ≤ ∞; are established.