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We find the exact order of the entropy numbers and the Kolmogorov widths of a class of functions defined by a condition on the uniform norm of blocks of the Fourier series taken over a lacunar sequence of indices. This result generalizes a result by B. S. Kashin and V. N. Temlyakov. [ABSTRACT FROM AUTHOR]

We establish a lower bound for the uniform norm of the trigonometric polynomial of special form via the sum of the L-norms of its summands. This result generalizes a theorem due to Kashin and Temlyakov, which, in turn, generalizes the classical Sidon inequality. [ABSTRACT FROM AUTHOR]