Logarithmic Bloch spaces in the polydisc, endpoint results for Hankel operators and pointwise multipliers

TL;DR

This paper introduces two types of Logarithmic Bloch spaces in the polydisc, characterizes bounded Hankel operators via symbols, and fully describes pointwise multipliers between these spaces, advancing the understanding of function spaces in several complex variables.

Contribution

It provides new definitions and equivalent characterizations of Logarithmic Bloch spaces and offers a complete description of pointwise multipliers in the polydisc setting.

Findings

Equivalent definitions of Logarithmic Bloch spaces in the polydisc

Characterization of bounded Hankel operators via symbols

Full description of pointwise multipliers between Bloch spaces

Abstract

We define two notions of Logarithmic Bloch space in the polydisc for which we provide equivalent definitions in terms of symbols of bounded Hankel operators. We also provide a full characterization of the pointwise multipliers between two different Bloch spaces of the unit polydisc.