Quantitative lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l^p$$\end{document}-Improving for Discrete Spherical Averages Along the Primes

We show quantitative (in terms of the radius) lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l^p$$\end{document}-improving estimates for the discrete spherical averages along the primes. These averaging operators were defined in [1] and are discrete, prime variants of Stein’s spherical averages. The proof uses a precise decomposition of the Fourier multiplier.