Necessary and Sufficient Conditions for Commutator of the Calderón–Zygmund Operator on Mixed-Norm Herz-Slice Spaces

Abstract

We obtain the separability of mixed-norm Herz-slice spaces, establish a weak convergence on mixed-norm Herz-slice spaces, and get the boundedness of the Calderón–Zygmund operator T on mixed-norm Herz-slice spaces. Moreover, we get the necessary and sufficient conditions for the boundedness of the commutator [b,T] on mixed-norm Herz-slice spaces, where b is a locally integrable function.

Keywords

• mixed-norm Herz-slice spaces
• BMO(ℝ^<i>n</i>)
• Calderón–Zygmund operator