Trigonometric and linear widths for the classes of periodic multivariable functions - Romanyuk, A. S. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We establish the exact-order estimates for the trigonometric widths of Nikol’skii – Besov $B^r_{∞ ,θ}$ and Sobolev $W^r_{∞, α} $ classesof periodic multivariable functions in the space $L_q,\; 1 < q < ∞$. The behavior of the linear widths of Nikol’skii – Besov $B^r_{∞ ,θ}$ classes in the space $L_q$ is investigated for certain relations between the parameters $p$ and $q$.