Bσ TYPE MIXED MORREY SPACES AND THEIR APPLICATIONS

This paper defines and studies the B-sigma type mixed Morrey spaces. Furthermore, we introduce the predual spaces of B-sigma type mixed Morrey spaces to establish the extrapolation theorem. As applications of extrapolation theory, we character the BMO space in different ways. On the one hand, we character the BMO spaces by the new John-Nirenberg inequality in terms of B(sigma )type mixed Morrey spaces. On the other hand, we establish the characterization of BMO spaces by the boundedness of commutators of the singular integral operator on B-sigma type mixed Morrey spaces.