Essential norms of composition operators and multipliers acting between different Hardy spaces

TL;DR

This paper investigates the essential norms of various operators, including inclusion, composition, and multipliers, acting between subspaces of different L^p and L^q spaces, providing new insights into their boundedness and compactness properties.

Contribution

It introduces explicit computations of the essential norms for these operators between subspaces of different L^p and L^q spaces, extending existing theory.

Findings

Explicit formulas for essential norms of inclusion operators

Characterization of when composition operators are compact

Conditions for multipliers to be bounded between subspaces

Abstract

We compute the essential norm of inclusion operators, composition operators and multipliers acting from a closed subspace of some $L^p$-space into a subspace of some $L^q$-space, with $p > q.$