On the Hardy - Littlewood majorant
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چکیده
منابع مشابه
On the Hardy–Littlewood Majorant Problem
Let Λ ⊆ {1, . . . , N}, and let {an}n∈Λ be a sequence with |an| ≤ 1 for all n. It is easy to see that ∥∥∥∥ ∑ n∈Λ ane(nθ) ∥∥∥∥ p ≤ ∥∥∥∥ ∑ n∈Λ e(nθ) ∥∥∥∥ p for every even integer p. We give an example which shows that this statement can fail rather dramatically when p is not an even integer. This answers in the negative a question known as the Hardy-Littlewood majorant conjecture, thereby ruling ...
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