A new type of Littlewood-Paley partition

Kathryn E. Hare Department of Pure Mathematics, University of Waterloo Ivo Klemes Department of Mathematics and Statistics, McGill University

TBD mathscidoc:1701.332775

Arkiv for Matematik, 30, (1), 297-309, 1990.12
We define a partition of Z into intervals {$I$_{j}} and prove the Littlewood-Paley inequality ‖$f$‖_{$p$}≦$C$_{p}‖$Sf$‖_{$p$}, 2≦$p$<∞. Here$f$is a function on [o, 2π) and $$Sf = (\sum |\Delta _j |^2 )^{1/2} , \hat \Delta j = \hat f\chi _{Ij} $$ . This is a new example of a partition having the Littlewood-Paley property since the {$I$_{j}} are not of the type obtained by iterating lacunary partitions finitely many times.
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@inproceedings{kathryn1990a,
  title={A new type of Littlewood-Paley partition},
  author={Kathryn E. Hare, and Ivo Klemes},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203538409009584},
  booktitle={Arkiv for Matematik},
  volume={30},
  number={1},
  pages={297-309},
  year={1990},
}
Kathryn E. Hare, and Ivo Klemes. A new type of Littlewood-Paley partition. 1990. Vol. 30. In Arkiv for Matematik. pp.297-309. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203538409009584.
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