Good Modulating Sequences for the Ergodic Hilbert Transform

TL;DR

This paper identifies classes of bounded sequences, including Besicovitch sequences with a rate condition, that are universally effective for the ergodic Hilbert transform across various L_p-spaces.

Contribution

It introduces and analyzes specific classes of sequences, notably Besicovitch sequences with a rate condition, as universally good for the ergodic Hilbert transform.

Findings

Besicovitch sequences with a rate condition are effective for the ergodic Hilbert transform.

The class of bounded sequences satisfying certain conditions is universally good in L_p-spaces.

The study extends understanding of sequence classes suitable for ergodic transforms.

Abstract

This article investigates classes of bounded sequences of complex numbers that are universally good for the ergodic Hilbert transform in L_p-spaces, 2\leq p\leq \infty : The class of bounded Besicovitch sequences satisfying a rate condition is among such sequence classes.