Universally L^1-Bad Arithmetic Sequences

Patrick LaVictoire

Universally L^1-Bad Arithmetic Sequences

Dynamical Systems 2011-08-26 v2 Classical Analysis and ODEs

Authors: Patrick LaVictoire

Abstract

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.

Cite

@article{arxiv.0905.3865,
  title  = {Universally L^1-Bad Arithmetic Sequences},
  author = {Patrick LaVictoire},
  journal= {arXiv preprint arXiv:0905.3865},
  year   = {2011}
}