On the Ritt property and weak type maximal inequalities for convolution powers on $\ell ^1(\mathbb {Z})$
Volume 235 / 2016
Studia Mathematica 235 (2016), 47-85
MSC: Primary 47A35, 37A99; Secondary 60B15.
DOI: 10.4064/sm8516-8-2016
Published online: 10 October 2016
Abstract
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 $\mu $ is centred 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 $\ell ^1(\mathbb Z)$.
