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A logarithmic uncertainty principle for functions with radial symmetry
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society , First View
- Published online by Cambridge University Press:
- 31 March 2025, pp. 1-14
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In this paper, we prove a new uncertainty principle for functions with radial symmetry by differentiating a radial version of the Stein–Weiss inequality. The difficulty is to prove the differentiability in the limit of the best constant that unlike the general case it is not known. We provide also an integral alternative formula for the logarithmic weight
$(\log|\xi|)$ in Fourier domain.
