English

Level set estimates for the discrete frequency function

Classical Analysis and ODEs 2017-06-13 v1

Abstract

We introduce the discrete frequency function as a possible new approach to understanding the discrete Hardy-Littlewood maximal function. Considering that the discrete Hardy-Littlewood maximal function is given at each integer by the supremum of averages over intervals of integer length, we define the discrete frequency function at that integer as the value at which the supremum is attained. After verifying that the function is well-defined, we investigate size and smoothness properties of this function.

Keywords

Cite

@article{arxiv.1706.03546,
  title  = {Level set estimates for the discrete frequency function},
  author = {Faruk Temur},
  journal= {arXiv preprint arXiv:1706.03546},
  year   = {2017}
}
R2 v1 2026-06-22T20:15:53.919Z