##### Department of Mathematics,

University of California San Diego

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### Math 248 - Analysis

## Joseph Cima

#### UNC, Chapel Hill

## A generalization of the Cesaro integral operator to Hardy $(H^p )$ spaces

##### Abstract:

We introduce the Cesaro operator and trace its history. We define a generalization of this operator to all Hardy spaces $H^{p}$ (disc). We discuss the boundedness and compactness of such operators. We improve a result of Hardy and Littlewood on primitives of $H^{P}$ functions. One can compute the essential spectrum of a subspace of these operators .

Host: Peter Ebenfelt

### November 25, 2003

### 9:30 AM

### AP&M 6218

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