We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions $\widetilde{\varphi}_j$ and trigonometric polynomials $\varphi_j$. The class of such operators includes classical interpolation polynomials ($\widetilde\varphi_j$ is the Dirac delta function), Kantorovich-type operators ($\widetilde\varphi_j$ is a characteristic function), scaling expansions associated with wavelet constructions, and others. Under different compatibility conditions on $\widetilde\varphi_j$ and $\varphi_j$, we obtain upper and lower bound estimates for the $L_p$-error of approximation by quasi-interpolation operators in terms of the best and best one-sided approximation, classical and fractional moduli of smoothness, $K$-functionals, and other terms.

翻译：我们研究普通多变周期准内插操作员的近似特性,这些特性由分布/功能产生,由全局性价比和三角数多元值产生,这类操作员的类别包括典型的内插多数值(全局性价比),Dirac delta函数,Kantorovich类型操作员的近似特性(全局性价比),与波板构造有关的扩大,以及其他。在美元全局性价比和美元等不同兼容条件下,我们从优和最佳单面光滑、美元功能和其他条件的角度,从准内插操作员的优和最佳单面近似值、经典和小数模式的角度获得近似值的上下约束估计值。