ℓ^p(ℤ) -- boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems

2014/01/07 by Mariusz Mirek, Mirek, Mariusz
Mathematics · #Advanced Harmonic Analysis Research #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CA

paper · pdf · doi:10.48550/arxiv.1401.1361

We follow the notation used in 'Roth's Theorem in the Piatetski-Shapiro primes' arXiv:1305.0043

openalex publication_date 2014/01/07 · arxiv created 2014/01/26 · arxiv updated 2014/01/28 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We establish the first pointwise ergodic theorems along thin sets of prime numbers; a set with zero density with respect to the primes. For instance we will be able to achieve this with the Piatetski-Shapiro primes. Our methods will be robust enough to solve the ternary Goldbach problem for some thin sets of primes.

Citations

• Nombres premiers de la forme ⌊nc⌋
• The Pjateckiĭ-S̆apiro prime number theorem
• Roth's Theorem in the Piatetski-Shapiro primes

Related

• Pointwise ergodic theorems for some thin subsets of primes
• Weak-type (1,1) inequality for discrete maximal functions and pointwise ergodic theorems along thin arithmetic sets
• Roth's Theorem and the Hardy--Littlewood majorant problem for thin subsets of primes
• Cotlar's ergodic theorem along the prime numbers
• Pointwise ergodic theorems along fractional powers of primes