Essential norms of weighted composition operators between Hardy spaces $H^p$ and $H^q$ for $1\leq p,q \leq \infty$

TL;DR

This paper determines the essential norms of weighted composition operators between Hardy spaces for all parameter ranges, completing previous partial results and providing new estimates.

Contribution

It provides a comprehensive analysis and estimates of the essential norms of weighted composition operators between Hardy spaces for all p and q.

Findings

Complete characterization of essential norms for all p, q in Hardy spaces

New estimates for cases where p and q are equal or different

Extension of previous partial results in the literature

Abstract

We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces $H^p$ and $H^q$ for $1\leq p,q\leq\infty.$ In particular we give some estimates for the cases $1=p\leq q\leq\infty$ and $1\leq q<p\leq\infty.$