Relationship between Hardy spaces associated with different homogeneities and one-parameter Hardy spaces (Q2443708)

Summary: We prove that the Hardy spaces associated with different homogeneities \(H_{\mathrm{com}}^p\), \(0 < p < \infty\) are continuously embedded into the intersection of the isotropic Hardy spaces \(H^p_{\mathrm{iso}}\) and the nonisotropic Hardy spaces \(H^p_{\mathrm{non}}\). As a consequence, we obtain that any operator bounded from either \(H^p_{\mathrm{iso}}\) or \(H^p_{\mathrm{non}}\) into \(L^p\) must be bounded from \(H^p_{\mathrm{com}}\) to \(L^p\).