Boundedness of both discrete Hardy and Hardy-Littlewood maximal operators via Muckenhoupt weights (Q1983203)

This article studies the boundedness of discrete versions of the Hardy operator and the Hardy-Littlewood maximal operator in the setting of weighted Lebesgue spaces \(\ell^p_u\) with \(1<p<+\infty\) where \(u\) is a discrete Muckenhoupt weight which belongs to a Muckenhoupt class \(\mathcal{A}_p\). Theorem 8 studies the Hardy operator while the Hardy-Littlewood maximal operator is studied in Theorem 12. The objects and the techniques follow closely the ideas and arguments of the usual case \(\mathbb{R}^n\).