# Weighted Inequalities of Weak Type for the Fractional Integral Operator

### Y. Rakotondratsimba

Institut Polytechnique St. Louis, Cergy-Pontoise, France

## Abstract

Sufficient conditions on weights $u(\cdot)$ and $v(\cdot)$ are given in order that the usual fractional integral operator $I_{\alpha} (0 < \alpha < n)$ is bounded from the weighted Lebesgue space $L^p(v(x)dx)$ into weak-$L^p(u(x)dx)$, with $1 ≤ p < \infty$. As a consequence a characterization for this boundedness is obtained for a large class of weight functions which particularly contains radial monotone weights.

## Cite this article

Y. Rakotondratsimba, Weighted Inequalities of Weak Type for the Fractional Integral Operator. Z. Anal. Anwend. 17 (1998), no. 1, pp. 115–134

DOI 10.4171/ZAA/812