Generalized Cesàro operators in the disc algebra and in Hardy spaces

Generalized Cesàro operators \(C_t\) $C_t$ , for \(t\in [0,1)\) $t\in [0,1)$ , are investigated when they act on the disc algebra \(A({\mathbb {D}})\) $A(\mathbb{D})$ and on the Hardy spaces \(H^p\) $H^p$ , for \(1\le p \le \infty \) $1\le p\le \infty$ . We study the continuity, compactness, spectrum and point spectrum of \(C_t\) $C_t$ as well as their linear dynamics and mean ergodicity on these spaces.