57 citations · 172 across the 24 of their papers we have counts for
5 papers · 1 filter
A note on twisted discrete singular Radon transforms
Lillian B. Pierce
In this paper we consider three types of discrete operators stemming from singular Radon transforms. We first extend an result for translation invariant discrete singular…
On discrete fractional integral operators and mean values of Weyl Sums
Lillian B. Pierce
In this paper we prove new bounds for a discrete fractional integral operator by applying techniques motivated by the circle method of Hardy and Littlewood to th…
A note on discrete fractional integral operators on the Heisenberg group
Lillian B. Pierce
We consider the discrete analogue of a fractional integral operator on the Heisenberg group, for which we are able to prove nearly sharp results by means of a simple argument of a…
Discrete fractional Radon transforms and quadratic forms
Lillian B. Pierce
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete opera…
On a discrete version of Tanaka's theorem for maximal functions
Jonathan Bober, Emanuel Carneiro, Kevin Hughes +1
In this paper we prove a discrete version of Tanaka's Theorem \cite{Ta} for the Hardy-Littlewood maximal operator in dimension , both in the non-centered and centered cases. F…