Semigroups of composition operators in analytic Morrey spaces

TL;DR

This paper investigates semigroups of composition operators on analytic Morrey spaces, demonstrating their strong continuity properties and similarities to those on BMOA spaces, thereby advancing understanding of operator behavior in these function spaces.

Contribution

It establishes the strong continuity of semigroups of composition operators on analytic Morrey spaces, revealing their behavior parallels that on BMOA spaces, which was previously unexplored.

Findings

Semigroups are strongly continuous on analytic Morrey spaces.

Behavior of these semigroups is similar to that on BMOA.

Provides insights into operator dynamics in Morrey spaces.

Abstract

Analytic Morrey spaces belong to the class of function spaces which, like BMOA, are defined in terms of the degree of oscillation on the boundary of functions analytic in the unit disc. We consider semigroups of composition operators on these spaces and focus on the question of strong continuity. It is shown that these semigroups behave like on BMOA.