Boris Simonov

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In this paper we study embedding theorems of function classes, which are subclasses of Lp, 1 ≤ p ≤ ∞. To define these classes, we use the notion of best trigonometric approximation as well as that of a (λ, β)-derivative, which is the generalization of a fractional derivative. Estimates of best approximations of transformed Fourier series are obtained.
In this paper we survey recent developments over the last 25 years on the mixed fractional moduli of smoothness of periodic functions from Lp, 1 < p <∞. In particular, the paper includes monotonicity properties, equivalence and realization results, sharp Jackson, Marchaud, and Ul’yanov inequalities, interrelations between the moduli of smoothness, the(More)
In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol’skii class and the generalized Lipschitz class. To define the Weyl-Nikol’skii class, we use the concept of a (λ, β)-derivative, which is a(More)
In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the socalled generalized Weyl-Nikol’skii class and the generalized Lipschitz class. To define the Weyl-Nikol’skii class, we use the concept of a (λ, β)-derivative, which is a(More)
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