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}
}