Abstract
Let , and let be a sequence of positive numbers with . Denote by the class of all functions for which the best approximation by trigonometric polynomials satisfies the condition .In this paper the relation between best approximations in different metrics is studied. Necessary and sufficient conditions are found for the imbedding , where and are positive sequences with and .Furthermore, it is proved that the condition of P. L. Ul'janov is not only sufficient but is also necessary for the imbedding .The question of imbedding in the space of continuous functions is also considered.Bibliography: 7 titles.
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