Quantitative $l^p$-improving for discrete spherical averages along the primes
Classical Analysis and ODEs
2019-12-20 v2 Number Theory
Abstract
We show quantitative (in terms of the radius) -improving estimates for the discrete spherical averages along the primes. These averaging operators were defined by Anderson, Cook, Hughes and Kumchev and are discrete, prime variants of Stein's spherical averages. The proof uses a precise decomposition of the Fourier multiplier.
Cite
@article{arxiv.1812.05592,
title = {Quantitative $l^p$-improving for discrete spherical averages along the primes},
author = {Theresa C. Anderson},
journal= {arXiv preprint arXiv:1812.05592},
year = {2019}
}
Comments
Typos and errors fixed. Final version to appear in JFAA