Let L 0 (T ) be the set of real-valued periodic measurable functions, let ψ : R + → R + be a modulus of continuity (ψ ≠ 0) , and let
The following problems are investigated: the relationship between the rate of approximation of f by trigonometric polynomials in L ψ and the smoothness in L 1, the relationship between the moduli of continuity of f in L ψ and L 1 and the imbedding theorems for the classes Lip(α, ψ) in L 1, and the structure of functions from the class Lip(1, ψ).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 9, pp. 1214–1232, September, 2012.
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Pichugov, S.A. Smoothness of functions in the metric spaces L ψ . Ukr Math J 64, 1382–1402 (2013). https://doi.org/10.1007/s11253-013-0723-8
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DOI: https://doi.org/10.1007/s11253-013-0723-8