Let T be a Calderón-Zygmund operator, i.e. T is bounded on and has a kernel K which satisfies the estimates
Let P(x,y) be a real-valued polynomial. The main result is that the operator
is bounded from to , where the Hardy space is defined by means of atoms. F. Ricci and E. M. Stein [J. Funct. Anal. 73, 179-194 (1987; Zbl 0622.42010)] recently proved that Op is bounded on -spaces, .