Maximal Operators Associated to Multiplicative Characters
Allison Lewko, Mark Lewko
TL;DR
This paper investigates the behavior of maximal operators linked to multiplicative characters and demonstrates that a key inequality analogous to Carleson-Hunt does not hold in this context.
Contribution
It establishes the failure of the natural analogue of the Carleson-Hunt inequality for maximal operators associated with multiplicative characters.
Findings
The Carleson-Hunt inequality does not extend to multiplicative characters.
The failure highlights fundamental differences in harmonic analysis for multiplicative characters.
Results impact understanding of maximal operators in number theory and harmonic analysis.
Abstract
We show that the natural analogue of the Carleson-Hunt inequality fails for multiplicative characters.
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