A Note on the Fourier Transform of Fractal Measures
نویسنده
چکیده
We are interested in the behavior of the Fourier transform of measures with finite energy. It is easy to see that Iα(μ) <∞ does not imply any pointwise decay of |μ̂(ξ)| as |ξ| → ∞. However, in general, averages of μ̂(ξ) behave much better. Let Γ be a smooth submanifold of Rd and let νΓ be a smooth surface measure on Γ. One may ask the following general question: Fix α ∈ (0, d), and assume that Iα(μ) = 1. For which β > 0
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تاریخ انتشار 2003