A note on Weyl type discrete inequalities
The author used elementary methods to prove that for \(\alpha\geq0\), \(p\geq0\), \(q\geq1\) and for a sequence of real numbers \(\{u_n\}_{n=0}^m\) the inequality \[ \sum_{n=0}^{m-1}|u_n|^{p+q} \leq M \Bigl\{\sum_{n=0}^{m-1}a_n|u_n|^p \bigl(|u_n|m^{-1} + |u_{n+1}-u_n|\bigr)^q\Bigr\}^{1/q} \Bigl\{\sum_{n=0}^{m-1}b_n|u_n|^{p+q}\Bigr\}^{1/q'} \] holds with a constant \(M\) depending on \(\alpha\), \(p\), \(q\), and with certain coefficients \(a_n\), \(b_n\) depending on \(\alpha\) and \(q\). Letting \(m\to\infty\) for a particular choice of parameters and coefficients he obtained a discrete analogue of the Weyl inequality as a consequence.
scientific article; zbMATH DE number 710350