Fractional integrals and \(A_p\)-weights: a sharp estimate
This paper deals with an inequality with an \(A_p\) weight for Riesz potential of a function \(f: \mathbb{R}^n\to \mathbb{R}\) defined by \[ I_\alpha f(x)= \int_{\mathbb{R}^n} {f(y)\over |x-y|^{n-\alpha}}\,dy\qquad\text{for }x\in\mathbb{R}^n. \] The constant in the relevant inequality is known to depend on the \(A_p\) constant of the weight. The authors find the exact form of this dependence. In particular, they exhibit the optimal exponent for the \(A_p\) constant of the weight.
scientific article; zbMATH DE number 5638292
scientific article