Abstract
The paper finds best constants in a class of multiplicative inequalities with one-dimensional spatial variables ∥f(k)∥∞ ⩽ c(k, l)∥f∥(2l−2k−1)/2l∥f(l)∥(2k+1)/2l −½⩽k⩽l−½ where f is a periodic function with zero mean value, and the norms in the right-hand side of the expression are the L2-norms.
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