We provide a survey of properties of the Cesàro operator on Hardy and weighted Bergman spaces, along with its connections to semigroups of weighted composition operators. We also describe recent developments regarding Cesàro-like operators and indicate some open questions and directions of future research.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc75-0-14, author = {V. G. Miller}, title = {The Ces\`aro and related operators, a survey}, journal = {Banach Center Publications}, volume = {75}, year = {2007}, pages = {233-247}, zbl = {1128.47034}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc75-0-14} }
V. G. Miller. The Cesàro and related operators, a survey. Banach Center Publications, Tome 75 (2007) pp. 233-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc75-0-14/