We show that the Lusin area function and essentially all of its real-variable generalizations are pointwise dominated by an \lq\lq intrinsic\rq\rq\ square function, and that this latter function is, for all practical purposes, no larger than a \lq\lq generic\rq\rq square function.
"The intrinsic square function." Rev. Mat. Iberoamericana 23 (3) 771 - 791, Decembar, 2007.