On the Multiplication Operators from the Natural μ -Bloch-Type Space into Another Natural ω -Bloch-Type Space

Xiaoman Liu () and Yongmin Liu
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Xiaoman Liu: College of Sciences, Nanjing Agricultural University, Nanjing 210095, China
Yongmin Liu: School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

Mathematics, 2025, vol. 13, issue 20, 1-22

Abstract: This paper investigates the boundedness of multiplication operators M ψ between natural μ -Bloch-type spaces B μ , nat ( B X ) (or their little μ -Bloch counterparts) and natural ω -Bloch-type spaces B ω , nat ( B X ) on the unit ball B X of a complex Banach space X . We establish complete characterizations for the boundedness of M ψ under varying conditions on the weight functions μ and ω , including specific cases such as logarithmic and power-weighted Bloch spaces. The results extend classical operator theory to infinite-dimensional settings, unifying prior work on finite-dimensional domains.

Keywords: the multiplication operator; Fréchet derivative; natural μ -Bloch-type space; boundedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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