Generalized Cesàro operators on certain function spaces
Volume 98 / 2010
Annales Polonici Mathematici 98 (2010), 189-199
MSC: 30D45, 30D60, 33C05, 47B38.
DOI: 10.4064/ap98-2-6
Abstract
Motivated by some recent results by Li and Stević, in this paper we prove that a two-parameter family of Cesàro averaging operators ${\cal P}^{b, c}$ is bounded on the Dirichlet spaces ${\cal D}_{p, a}$. We also give a short and direct proof of boundedness of ${\cal P}^{b, c}$ on the Hardy space $H^p$ for $1< p< \infty$.
