Relationship between hardy spaces associated with different homogeneities and one-parameter Hardy spaces

We prove that the hardy spaces associated with different homogeneities hcom p,0 < p < ∞,are continuously embedded into the intersection of the isotropic hardy spaces hiso p and the nonisotropic hardy spaces hnon p. as a consequence,we obtain that any operator bounded from either h iso p or hnon p into lp must be bounded from hcom p to lp. © 2013 xinfeng wu.