Norms of inclusions between some spaces of analytic functions

TL;DR

This paper investigates the norms of inclusion operators between various analytic function spaces, providing explicit computations and asymptotic estimates where these norms were previously unknown.

Contribution

It offers new precise calculations and asymptotic estimates for the norms of inclusion operators among Besov, Bloch, and weighted Bergman spaces.

Findings

Computed norms of inclusion operators between specific spaces

Provided asymptotic estimates for these norms

Enhanced understanding of the structure of analytic function spaces

Abstract

The inclusions between the Besov spaces $B^q$, the Bloch space $\mathcal{B}$ and the standard weighted Bergman spaces $A^p_\alpha$ are completely understood, but the norms of the corresponding inclusion operators are in general unknown. In this work, we compute or estimate asymptotically the norms of these inclusions.