On some sharp estimates of Toeplitz operator in some spaces of Hardy-Lizorkin type of analytic functions in the polydisk

TL;DR

This paper establishes new sharp estimates for Toeplitz operators acting on specialized Hardy-Lizorkin type spaces of analytic functions in the polydisk, extending previous results in the field.

Contribution

It introduces novel sharp bounds for Toeplitz operators in new function spaces of several complex variables, broadening the understanding of their behavior.

Findings

Derived new sharp bounds for Toeplitz operators

Extended previous results to new function spaces

Enhanced understanding of operator behavior in multivariable settings

Abstract

We provide some new sharp assertions on the action of Toeplitz $T_\varphi$ operator in new $F^{p,q}_\alpha$ type spaces of analytic functions of several complex variables extending previously known assertions proved by various authors.