The ratio of the number of yellow circles to the number of white circles is 1 : 4. For each yellow circle there are 4 white circles. The ratio 3 : 12 is equivalent to 1 : 4 because for each yellow ...
Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become ...
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