Boundedness of the product of some operators from the natural Bloch space into weighted-type space

Abstract

Let $ \mathbb{B}_X $ be the unit ball of a complex Banach space $ X $, which may be infinite dimensional. The authors characterize the boundedness of the product of the radial derivative operator and the weighted composition operator from the natural Bloch space (or the little Bloch-type space) into the weighted-type space (or the little weighted-type space) on $ \mathbb{B}_X $.

Keywords

• weighted composition operator
• radial derivative operator
• natural bloch space
• weighted-type space
• boundedness