A Logarithmic Uncertainty Principle for Functions with Radial Symmetry

Abstract

In this note, 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.

arXiv comment10 pages

References in corpus (2)

• A surprising formula for Sobolev norms
• Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces