On the Ritt property and weak type maximal inequalities for convolution powers on ${\ell }^1(\mathbb{Z})$

Abstract

In this paper we study the behaviour of convolution powers of probability measures $\mu$ on $\mathbb{Z}$, such that $(\mu (n){)}_{n\in \mathbb{N}}$ is completely monotone or such that $\nu$ is centered with a second moment. In particular we exhibit many new examples of probability measures on $\mathbb{Z}$ having the so called Ritt property and whose convolution powers satisfy weak type maximal inequalities in ${\ell }^1(\mathbb{Z})$.

32 pages

Cited by in corpus (1)

• On discrete subordination of power bounded and Ritt operators