BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERON-ZYGMUND OPERATOR ON LORENTZ SPACE

In this paper, the authors consider the omega-type Calderon-Zygmund operator T-omega and the commutator [b, T-omega] generated by a symbol function b on the Lorentz space L-p,L-r (X) over the homogeneous space (X, d, mu). The boundedness and the compactness of the commutator [b, T-omega] on Lorentz space L-p,L-r (X) are founded for any p is an element of (1, infinity) and r is an element of [1, infinity).

Automated summary

This paper investigates the boundedness and compactness of the commutator [b, T-omega] generated by a symbol function b on the Lorentz space L-p,L-r (X), as well as the omega-type Calderon-Zygmund operator T-omega. The results hold for any p in the range (1, infinity) and r in the range [1, infinity).