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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 1, 1998, pp. 115–134
DOI: 10.4171/ZAA/812

Published online: 1998-03-31

Weighted Inequalities of Weak Type for the Fractional Integral Operator

Y. Rakotondratsimba[1]

(1) Institut Polytechnique St. Louis, Cergy-Pontoise, France

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.

Keywords: Fractional integral operators, weighted weak-type inequalities

Rakotondratsimba Y.: Weighted Inequalities of Weak Type for the Fractional Integral Operator. Z. Anal. Anwend. 17 (1998), 115-134. doi: 10.4171/ZAA/812