Multiplication operators between iterated logarithmic Lipschitz spaces of a tree

TL;DR

This paper characterizes bounded and compact multiplication operators between various iterated logarithmic Lipschitz spaces on an infinite tree, providing norm estimates and showing the absence of isometries.

Contribution

It offers a new characterization of bounded and compact multiplication operators between iterated logarithmic Lipschitz spaces and weighted Lipschitz spaces on an infinite tree.

Findings

Characterization of bounded multiplication operators

Characterization of compact multiplication operators

No isometries exist among these operators

Abstract

In this article, we characterize the bounded and the compact multiplication operators between distinct iterated logarithmic Lipschitz spaces, and between the Lipschitz space and an iterated logarithmic Lipschitz space of an infinite tree. In addition, we provide operator norm estimates and show that there are no isometries among such operators. %We obtain a new characterization of the bounded multiplication operators acting on an iterated logarithmic Lipschitz space and the compact multiplication operators between the weighted Lipschitz space and the Lipschitz space.