A note about the l^p-improving property of the average operators

2019/10/28 by J. A. Jiménez Madrid, Madrid, José
Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1910.12448

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

Abstract

In this paper we give a short proof of the ℓ^p-improving property of the average operator along the square integers and more general quadratic polynomials. Moreover we obtain a similar result for some higher degree polynomials. We also show an elementary proof of the ℓ^p-improving property of the average operator along primes.

Citations

• ℓ^p-improving for discrete spherical averages
• Averages Along the Primes: Improving and Sparse Bounds

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