Hardy operators and the commutators on Hardy spaces

Abstract

Abstract In this paper, the boundedness of the classic Hardy operator and its adjoint on Hardy spaces is obtained. We also discuss the boundedness for the commutators generated by the classic Hardy operator and its adjoint with B M O $BMO$ and C M O ( R + ) $CMO(\mathbb{R}^{+})$ functions on Hardy spaces.

Keywords

• Hardy operator
• Commutators
• B M O $BMO$
• C M O $CMO$
• Hardy space