7 papers · 1 filter
The higher regularity of the discrete Hardy-Littlewood maximal function
Faruk Temur, Hikmet Burak Özcan
In a recent short note the first author gave the first positive result on the higher order regularity of the discrete noncentered Hardy-Littlewood maximal function. In this article…
Random exponential sums and lattice points in regions
Faruk Temur, Cihan Sahillioğulları
In this article we study two fundamental problems on exponential sums via randomization of frequencies with stochastic processes. These are the Hardy-Littlewood majorant problem, a…
Discrete fractional integrals, lattice points on short arcs, and diophantine approximation
Faruk Temur
Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the sc…
The frequency function and its connections to the Lebesgue points and the Hardy-Littlewood maximal function
Faruk Temur
The aim of this work is to extend the recent work of the author on the discrete frequency function to the more delicate continuous frequency function , and further to…
Discrete fractional integral operators with binary quadratic forms as phase polynomials
Faruk Temur, Ezgi Sert
We give estimates on discrete fractional integral operators along binary quadratic forms. These operators have been studied for 30 years starting with the investigations of Arkhipo…
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-Littlew…