Abstract
In this paper the author studies classesHqΩ of periodic functions of several variables whose mixed moduli of continuity do not exceed a given modulus of continuity ω(t1 ...,td). Necessary and sufficient conditions of belonging of a functionf(x1, ...,xd) to the classHqΩ are considered (Theorem 1). These necessary and sufficient conditions are proved under some additional assumptions on ω(t1, ...,td). It is shown that additional assumptions cannot be omitted (Theorem 3). Besides, the estimates of best approximations of classesHqΩ with some special ω(t1, ...,td) are given (Theorems 4 and 5).
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