A radial integrability result concerning bounded functions in analytic Besov spaces with applications

TL;DR

This paper constructs bounded functions in analytic Besov spaces with poorly integrable derivatives along every radius, revealing new insights into the structure of these spaces and their operators.

Contribution

It demonstrates the existence of bounded functions with badly integrable derivatives in all $B^p$ spaces, and applies this to study multipliers and superposition operators.

Findings

Existence of bounded functions with badly integrable derivatives in $B^p$

Applications to multipliers on $B^p$

Applications to weighted superposition operators

Abstract

We prove that for every $p\ge 1$ there exists a bounded function in the analytic Besov space $B^p$ whose derivative is "badly integrable", along every radius. We apply this result to study multipliers and weighted superposition operators acting on the spaces $B^p$.