JournalszaaVol. 17, No. 1pp. 115–134

Weighted Inequalities of Weak Type for the Fractional Integral Operator

  • Y. Rakotondratsimba

    Institut Polytechnique St. Louis, Cergy-Pontoise, France
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Abstract

Sufficient conditions on weights u()u(\cdot) and v()v(\cdot) are given in order that the usual fractional integral operator Iα(0<α<n)I_{\alpha} (0 < \alpha < n) is bounded from the weighted Lebesgue space Lp(v(x)dx)L^p(v(x)dx) into weak-Lp(u(x)dx)L^p(u(x)dx), with 1p<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