Abstract
We establish the exact-order estimates for the trigonometric widths of Nikol’skii–Besov $$ {B}_{\infty, \theta}^r $$ and Sobolev $$ {W}_{\infty, \alpha}^r $$ classes of periodic multivariate functions in the space L q , 1 < q < 1. The behavior of the linear widths of Nikol’skii–Besov $$ {B}_{p,\theta}^r $$ classes in the space L q is investigated for some relations between the parameters p and q.
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