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math.CA2021
Optimal weak estimates for Riesz potentials
Liang Huang, Hanli Tang
In this note we prove a sharp reverse weak estimate for Riesz potentials $$\|I_{s}(f)\|_{L^{\frac{n}{n-s},\infty}}\geq γ_sv_{n}^{\frac{n-s}{n}}\|f\|_{L^1}~~\text{for}~~0<f\in {L^1(…
math.AP2021
Reverse conformally invariant Sobolev inequalities on the sphere
Rupert L. Frank, Tobias König, Hanli Tang
We consider the optimization problem corresponding to the sharp constant in a conformally invariant Sobolev inequality on the -sphere involving an operator of order . In…