Lillian B. Pierce

collaborators

3 papers

math.CA2023

Generalizations of the Schrödinger maximal operator: building arithmetic counterexamples

Rena Chu, Lillian B. Pierce

Let $T_{t}^{P_{2}} f (x)$ denote the solution to the linear Schrödinger equation at time $t$ , with initial value function $f$ , where $P_{2} (ξ) = ∣ ξ ∣^{2}$ . In 1980, Carleson asked for the mi…

math.CA2010

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 $ℓ^{p}$ result for translation invariant discrete singular…

math.NT2010

On discrete fractional integral operators and mean values of Weyl Sums

Lillian B. Pierce

In this paper we prove new $(ℓ^{p}, ℓ^{q})$ bounds for a discrete fractional integral operator by applying techniques motivated by the circle method of Hardy and Littlewood to th…