15 citations · 17 across the 14 of their papers we have counts for
12 papers · 1 filter
The square function estimate for the cone in four dimensions
Faruk Temur
We obtain the reverse square function estimate for the light cone in four dimensions from the critical local-smoothing and round-cone propagation statements in the September…
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…
The second derivative of the discrete Hardy-Littlewood maximal function
Faruk Temur
The regularity of the Hardy-Littlewood maximal function, in both discrete and continuous contexts, and for both centered and noncentered variants, has been subjected to intense stu…
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…
A quantitative Balian-Low theorem for higher dimensions
Faruk Temur
We extend the quantitative Balian-Low theorem of Nitzan and Olsen to higher dimensions.
On regularity of the discrete Hardy-Littlewood maximal function
Faruk Temur
We extend the recent boundedness result of Kurka for Hardy-Littlewood maximal function to discrete setting.
An endline bilinear cone restriction estimate for mixed norms
Faruk Temur
We prove an bilinear Fourier extension estimate for the cone when are on the critical line . This extends…
A Fourier restriction estimate for surfaces of positive curvature in R^6
Faruk Temur
We improve the best known exponent for the restriction conjecture in R^6. Our idea is applicable to any dimension n satisfying n = 0 mod 3, though we do not explicitly calculate th…