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Maximal Operators Associated to Multiplicative Characters
Allison Lewko, Mark Lewko
We show that the natural analogue of the Carleson-Hunt inequality fails for multiplicative characters.
A Variational Barban-Davenport-Halberstam Theorem
Allison Lewko, Mark Lewko
We prove variational forms of the Barban-Davenport-Halberstam Theorem and the large sieve inequality. We apply our result to prove an estimate for the sum of the squares of prime d…
An Exact Asymptotic for the Square Variation of Partial Sum Processes
Allison Lewko, Mark Lewko
We establish an exact asymptotic formula for the square variation of certain partial sum processes. Let be a sequence of independent, identically distributed mean zero…
Estimates for the Square Variation of Partial Sums of Fourier Series and their Rearrangements
Allison Lewko, Mark Lewko
We investigate the square variation operator (which majorizes the partial sum maximal operator) on general orthonormal systems (ONS) of size . We prove that the norm…