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

If T 1 and T 2 are two singular integral operators associated with isotropic and anisotropic homogeneity, respectively, then T 1 , T 2 and T 1 ∘ T 2 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.