J. Aust. Math. Soc.  79 (2005), 77-94
Two weight norm inequalities for commutators of one-sided singular integrals and the one-sided discrete square function

M. Lorente
  Análisis Matemático
  Facultad de Ciencias
  Universidad de Málaga
  29071 Málaga
  Spain
  lorente@anamat.cie.uma.es
and
M. S. Riveros
  FaMAF
  Universidad Nacional de Córdoba
  CIEM (CONICET)
  5000 Córdoba
  Argentina
  sriveros@mate.uncor.edu


Abstract
The purpose of this paper is to prove strong type inequalities with pairs of related weights for commutators of one-sided singular integrals (given by a Calderón-Zygmund kernel with support in $(-\infty, 0)$) and the one-sided discrete square function. The estimate given by C. Segovia and J. L. Torrea is improved for these one-sided operators giving a wider class of weights for which the inequality holds.
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