Cesàro-Type Operators Acting on the Drury-Arveson Space

Abstract

The celebrated Cesàro operator is a well-known operator with interesting connections to a variety of objects in operator theory. Generalizations have been made for Cesàro-type operators acting on weighted Hardy spaces but constructing analogs of the Cesàro operator for function spaces of several complex variables such as the Drury-Arveson space has yet to be achieved. In this article, we posit a definition we belief is the correct generalization to several variables and establish a few of its basic properties.