Universally L^1-Bad Arithmetic Sequences

Details Universally L^1-Bad Arithmetic Sequences Universally L^1-Bad Arithmetic Sequences

2009-05-25

arxiv.org/abs/0905.3865v2

J. Anal. Math. 113 (2011), 241-263

Mathematics

Dynamical Systems

LaTeX, 18 pages; changed some notation and repaired typos

Scientific paper

We present a modified version of Buczolich and Mauldin's proof that the
sequence of square numbers is universally L^1-bad. We extend this result to a
large class of sequences, including the dth powers and the set of primes;
furthermore, we show that any subsequence of the averages taken along these
sequences is also universally L^1-bad.

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