The common Hardy space and BMO space for singular integral operators associated with isotropic and anisotropic homogeneity

If T1 and T2 are two singular integral operators associated with isotropic and anisotropic homogeneity, respectively, then T1, T2 and T1∘T2 are bounded on different Hardy spaces and BMO spaces (see [7], [8], [12]). In our paper, we show that these operators are actually bounded on a common Hardy space and a common BMO space.