Fractional operators on the bounded symmetric domains of the Bergman spaces

Abstract

Mathematics has several uses for operators on bounded symmetric domains of Bergman spaces including complex geometry, functional analysis, harmonic analysis and operator theory. They offer instruments for examining the interaction between complex function theory and the underlying domain geometry. Here, we extend the Atangana-Baleanu fractional differential operator acting on a special type of class of analytic functions with the m-fold symmetry characteristic in a bounded symmetric domain (we suggest the open unit disk). We explore the most significant geometric properties, including convexity and star-likeness. The boundedness in the weighted Bergman and the convex Bergman spaces associated with a bounded symmetric domain is investigated. A dual relations exist in these spaces. The subordination and superordination inequalities are presented. Our method is based on Young's convolution inequality.

Keywords

• univalent function
• subordination
• superordination
• open unit disk
• fractional calculus
• fractional differential operator
• analytic function
• fractional differential equation
• symmetric domain