We consider the vector-valued extension of the Fefferman-Stein-Strömberg sharp maximal inequality under growth condition. As an application we obtain a vector-valued extension of the boundedness of the commutator. Furthermore, we prove the boundedness of the commutator.
Weighted norm inequality, non-doubling (nonhomogeneous), sharp-maximal function, commutator.
MSC 2000: 42B35, 42B25