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

Abstract

In this paper we give a short proof of the ${\ell }^p$-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 ${\ell }^p$-improving property of the average operator along primes.

9 pages