A characterization of C(M) over dotO(q)over-right-arrow via the commutator of Hardy-type operators on mixed Herz spaces

In this paper, we introduce and study the mixed central bounded mean oscillation space C(M) over dotO((q) over right arrow)(R-n), which is a new central version of the bounded mean oscillation spaces BMO. The pre-dual of C(M) over dotO((q) over right arrow)(R-n) is proved to be the mixed Herz- Hardy space HA((q) over right arrow)(R-n). Moreover, we also give a characterization of C(M) over dotO((q) over right arrow)(R-n) via the boundedness of the commutators of ndimensional Hardy operator and its dual operator on mixed Herz spaces. (K) over dot((q) over right arrow)(alpha p)(R-n).

Automated summary

This paper introduces and studies the mixed central bounded mean oscillation space C(M), showing its relationship with the mixed Herz-Hardy space HA. The characterization of C(M) is given based on the boundedness of certain commutators involving ndimensional Hardy operator and its dual operator.