Level Set Estimates for the Discrete Frequency Function

  • Faruk Temur


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.


Hardy–Littlewood maximal function Frequency function Averaging operators Integral operators Optimal intervals 

Mathematics Subject Classification

Primary 42B25 Secondary 46E35 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIzmir Institute of TechnologyIzmirTurkey

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