2023/05/08 by Santiago Boza, Javier Soria · 1 citation
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Advanced Banach Space Theory
paper · doi:10.1016/j.jat.2023.105911
Recently, several authors have considered the problem of determining optimal norm inequalities for discrete Hardy-type operators (like Cesàro or Copson). In this work, we obtain sharp bounds for the norms of the difference of the Cesàro operator with either the identity or the shift, when they are restricted to the cone of decreasing sequences in ℓp (which is closely related to the previously mentioned estimates). Finally, we also address the case of weighted inequalities and find an interesting contrast between the norms of these two difference operators.