Boundedness of composition operators with mixed homogeneities

Suppose that T1 is a Calderon–Zygmund operator with isotropic homogeneity and T2 is a Calderon–Zygmund operator with non‐isotropic homogeneity. In this note, the boundedness of the composition operator T1∘T2 on the Hardy space is presented. The results in this paper extend earlier related results on convolution operators to non‐convolution setting.