Vector-Valued Herz Spaces and Herz-Type Hardy Spaces

摘要

In tin's paper, we introduce vector-valued Herz spaces and Herz-type Hardy spaces, and vector-valued function spaces of central mean oscillation. The corresponding scalar-valued results are extended to the vector-valued case, respectively. For example, the Riesz transforms are proved to be bounded from HK_X~p to K_X~p, if X is a UMD space; and the dual space of HK_X~p is the space CSMOP_(X~*)~(p') if X~* has the Radon-Nikydom property, where 1 < p < ∞ and 1/p+l/p' = 1. Finally, we obtain the grand maximal characterization and molecule decomposition characterization of these vector-valued Herz-type Hardy spaces.