On some new sharp results on Toeplits operators in the unit disk

TL;DR

This paper presents new sharp results on the behavior of Toeplitz operators acting between Triebel, Besov, and BMOA-type spaces on the unit disk, extending previous work to the case s ≥ 1.

Contribution

It extends existing results on Toeplitz operators to the case s ≥ 1, with minor modifications to previous proofs, broadening understanding of their action on various function spaces.

Findings

Established sharp bounds for Toeplitz operators in the s ≥ 1 case.

Extended the analysis of Toeplitz operators to new BMOA-type spaces.

Refined proof techniques from earlier studies.

Abstract

We provide new sharp results on the action of Toeplitz operators from Triebel and Besov spaces to new BMOA-type function spaces on the unit disk. In this paper we consider $s\geq 1$ case in previous papers $s<1$ was covered for $BMOA_{s,q}$ and $BMOA_{s}^p$ spaces. We modify a little our previously known proofs.