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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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 5, pp. 670–681, May, 2017.

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Romanyuk, A.S. Trigonometric and Linear Widths for the Classes of Periodic Multivariate Functions.
*Ukr Math J* **69**, 782–795 (2017). https://doi.org/10.1007/s11253-017-1395-6

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DOI: https://doi.org/10.1007/s11253-017-1395-6