Isometries of the Derivative Zygmund F-Algebra of Analytic Functions on the Unit Disk

Key Points

• The main aim is to characterize linear and multiplicative isometries of a novel space of analytic functions.
• Introduced a space of analytic functions with derivatives in the Zygmund F-algebra.
• Characterization of linear and multiplicative isometries was provided.
• Investigated isometric multipliers and zero divisors as an application.
• Characterized linear isometries and multiplicative isometries explicitly.
• Identified conditions under which isometric multipliers exist.
• Explored properties of zero divisors in the defined analytic functions space.