We consider an abstract analogue of $S_{\la}^{\#}f$, the truncated square function introduced by J.-O. Str\"omberg, and show that it is closely related to operators appearing in the theory of tent spaces. We suggest an approach to basic results for these spaces which differs from that due to R.R. Coifman, Y. Meyer and E.M. Stein. Also we discuss pointwise estimates involving $S_{\la}^{\#}f$ as well as different variants of sharp maximal functions.