Let μ, be a positive Radon measure with compact support in the euclidean n-space ℝn. Introducing the Fourier transform
and the averages over the spheres
we can write the α-energy, 0 < α < n, of μ as
where the positive constants c1 and c2 depend only on n and α. The second equality is based on the Plancherel formula and the fact that where .
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