Maximal functions and multipliers for subkernels of Toeplitz operators

TL;DR

This paper explores the relationships between maximal functions and multipliers within Toeplitz kernels and subkernels, providing new model space representations for these operators.

Contribution

It introduces novel relations between maximal functions and multipliers in Toeplitz kernels, leading to new isometric and Hayashi's model space representations.

Findings

Established relations between maximal functions in Toeplitz kernels and subkernels

Derived new model space representations for Toeplitz kernels

Enhanced understanding of multipliers' actions on subkernels

Abstract

We study the relations between maximal functions in a Toeplitz kernel and those in a subkernel of the same Toeplitz operator, as well as the question of how multipliers between Toeplitz kernels act on subkernels. We use those relations to obtain model space representations, in particular isometric model space representations and Hayashi's representation, for some important classes of Toeplitz kernels.