The norms of the images of multiplier type operators generated by an arbitrary generator are estimated in terms of the best approximations of univariate periodic functions by trigonometric polynomials in the -spaces, . As corollaries, estimates for the quality of approximation by Fourier means, an inverse theorem of approximation theory, comparison theorems, an analogue of the Marchaud inequality for generalized moduli of smoothness defined by a periodic generator, as well as some constructive sufficient conditions for generalized smoothness and Bernstein type inequalities for generalized derivatives of trigonometric polynomials are obtained.

Bibliography: 49 titles.

由任意生成器生成的乘法器类型算子的图像的范数是根据单变量周期函数的最佳近似值通过 空间中的三角多项式估计的。作为推论，通过傅立叶方法对近似质量的估计、近似理论的逆定理、比较定理、由周期生成器定义的广义平滑度模的 Marchaud 不等式的类似物，以及广义平滑度的一些建设性充分条件获得了三角多项式的广义导数的 Bernstein 型不等式。

参考书目：49 个。