Isometric composition operators on the analytic Besov spaces

TL;DR

This paper characterizes isometric composition operators on analytic Besov spaces, showing they are induced by rotations for certain p-values and extending previous results for others, including spaces with equivalent norms.

Contribution

It provides a complete characterization of isometric composition operators on analytic Besov spaces for all p, including new results for p>2 and spaces with equivalent norms.

Findings

Isometric composition operators for 1<p<2 are rotations.

Extended characterization for p>2.

Analyzed isometries on Besov spaces with equivalent norms.

Abstract

We investigate the isometric composition operators on the analytic Besov spaces. For $1<p<2$ we show that an isometric composition operator is induced only by a rotation of the disk. For $p>2$, we extend previous work on the subject. Finally, we analyze this same problem for the Besov spaces with an equivalent norm.