Multidimensional inequalities between distinct metrics in spaces with an asymmetric normстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Jackson-Nikol'skii inequalities in the spaces L-p1,(p2)(T-d) and L-p1,(p2) (R-d) endowed with asymmetric norms are studied for trigonometric polynomials and entire functions of exponential type, respectively. It is shown that for any d epsilon N, n epsilon N-d, and p1, p2, q1, q2 epsilon (0, infinity] a trigonometric polynomial T-n of degree n(j) in x(j) satisfies the inequality [GRAPHICS] where C-p1,(p2),(q1),(q2),d is a constant independent of n and psi is an explicitly indicated function. Examples of polynomials show that this estimate is sharp in order. A. similar result is obtained for functions of exponential type.