Inequalities for analytic functions with the derivative in H1

TL;DR

This paper establishes a new inequality related to analytic functions with derivatives in H1, providing a simplified proof of a theorem on bounded Toeplitz operators in the unit disc.

Contribution

It introduces an integrated Hardy-type inequality and applies it to simplify the proof of a theorem on Toeplitz operators.

Findings

Proved an integrated Hardy inequality for analytic functions.

Simplified the proof of Vinogradov's theorem on Toeplitz operators.

Enhanced understanding of inequalities in analytic function spaces.

Abstract

It is proved an inequality - integrated analogue of the Hardy inequality and as application simplified proof of the theorem of S. A. Vinogradov for the bounded Toeplitz operators on the space of functions analytic and bounded in the unit disc is given.