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

Let T be a strongly singular Calderon-Zygmund operator and b is an element of L-loc (R-n). This article finds out a class of non-trivial subspaces BMO omega,p,u (R-n) of BMO (R-n) for certain omega is an element of A(1), 0 < p <= 1 and 1 < u <= infinity, such that the commutator [b, T] is bounded from weighted Hardy space H-omega(p) (R-n) to weighted Lebesgue space L-omega(p)(R-n) if b is an element of BMO omega,p,infinity (R-n), and is bounded from weighted Hardy space H-omega(p)(R-n) to itself if T*1 = 0 and b is an element of BMO omega,p,u (R-n) for 1 < u < 2.