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

Christophe Cuny

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arXiv · 1601.05618

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

Christophe Cuny

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Abstract

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

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Christophe Cuny. 2016-01-21. On the Ritt property and weak type maximal inequalities for convolution powers on $\ell^1(\Z)$. https://arxiv.org/abs/1601.05618

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