The Commutators of Strongly Singular Integral Operators on the Weighted Hardy Spaces

Let T be a strongly singular Calderón-Zygmund operator and b ∈ Lloc（R~n）. This article finds out a class of non-trivial subspaces BMOω,p,u（R~n） of BMO（R~n） for certain ω∈ A1, 0 < p ≤ 1 and 1 < u ≤∞, such that the commutator [b, T ] is bounded from weighted Hardy space Hωp（R~n） to weighted Lebesgue space Lωp（R~n） if b ∈ BMOω,p,∞（R~n）, and is bounded from weighted Hardy space Hωp（R~n） to itself if T*1 = 0 and b ∈ BMOω,p,u（R~n） for 1 < u < 2.