Thickness conditions and Littlewood--Paley sets
Vladimir Lebedev
TL;DR
This paper investigates the maximal thickness of sets on the real line that possess Littlewood--Paley properties, exploring the relationship between set density and harmonic analysis conditions.
Contribution
It provides new bounds and insights into the thickness of sets with Littlewood--Paley properties, advancing understanding in harmonic analysis.
Findings
Established upper bounds on the thickness of LP sets
Identified conditions under which sets with LP properties can be dense
Extended previous results on Littlewood--Paley sets in real analysis
Abstract
We consider sets in the real line that have Littlewood--Paley properties or and study the following question: How thick can these sets be?
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