Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 62426, 10 pages

Weighted weak-type inequalities for generalized Hardy operators

A. L. Bernardis,1 F. J. Martín-Reyes,2 and P. Ortega Salvador2

1IMAL-CONICET, Güemes 3450, Santa Fe 3000, Argentina
2Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Málaga 29071, Spain

Received 13 June 2006; Accepted 21 September 2006

Copyright © 2006 A. L. Bernardis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We characterize the pairs of weights (v,w) for which the Hardy-Steklov-type operator Tf(x)=g(x)s(x)h(x)K(x,y)f(y)dy applies Lp(v) into weak-Lq(w), q<p, assuming certain monotonicity conditions on g, s, h, and K.