# Article

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Keywords:
Weyl fractional integrals; weights
Summary:
In this paper we give a sufficient condition on the pair of weights $(w,v)$ for the boundedness of the Weyl fractional integral $I_{\alpha}^+$ from $L^p(v)$ into $L^p(w)$. Under some restrictions on $w$ and $v$, this condition is also necessary. Besides, it allows us to show that for any $p: 1 \leq p < \infty$ there exist non-trivial weights $w$ such that $I_{\alpha}^+$ is bounded from $L^p(w)$ into itself, even in the case $\alpha > 1$.
References:
[1] Bennett C., Sharpley R.: Interpolation of Operators. Academic Press, 1988. MR 0928802 | Zbl 0647.46057
[2] García-Cuerva J., Rubio de Francia J.L.: Weighted Norm Inequalities and Related Topics. North-Holland, 1985. MR 0848147
[3] Hernández e.: Weighted inequalities through factorization. Publ. Mat. 35 (1991), 141-153. MR 1103612
[4] Lorente M., de la Torre A.: Weighted inequalities for some one-sided operators. Proc. Amer. Math. Soc. 124 (1996), 839-848. MR 1317510 | Zbl 0895.26002
[5] Martín Reyes F.J., Sawyer E.: Weighted inequalities for Riemann-Liouville fractional integrals of order one and greater. Proc. Amer. Math. Soc. 106 (3) (1989), 727-733. MR 0965246
[6] Verbitsky I.E., Wheeden R.L.: Weighted trace inequalities for fractional integrals and applications to semilinear equations. J. Funct. Anal. 129 (1) (1995), 221-241. MR 1322649 | Zbl 0830.46029

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