Discrete Fractional Integration Operators Along the Primes

2019/05/07 by Ben Krause, Krause, Ben
Mathematics · #Advanced Harmonic Analysis Research #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1905.02767

openalex publication_date 2019/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the discrete fractional integration operators along the primes T^λ_ℙf(x) := ∑_p (f(x-p))/(p^λ) ⋅ log p are bounded ℓ^p→ ℓ^p' whenever (1)/(p') < (1)/(p) - (1-λ), p > 1. Here, the sum runs only over prime p.

Related

• On discrete fractional integral operators and mean values of Weyl Sums
• A Discrete Carleson Theorem Along the Primes with a Restricted Supremum
• On Some Multipliers Related to Discrete Fractional Integrals
• Pseudo-differential operators on ℤⁿ with applications to discrete fractional integral operators
• Fractional series operators on discrete Hardy spaces