Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 62426, 10 pages
doi:10.1155/JIA/2006/62426

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

Abstract

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.