chapter  4
4 Pages

The Hardy space, Szego˝ projection, and Kerzman-Stein formula

Let A∞(bΩ) denote the set of functions on bΩ that are the boundary values of functions in A∞(Ω). The Hardy space, H2(bΩ), is defined to be the closure in L2(bΩ) of A∞(bΩ). (This is not the standard definition of the Hardy space given in, say Stein [St], however, we will explain later why it is equivalent to any of the more standard definitions.) To streamline our notation, we will identify the space A∞(Ω) with A∞(bΩ).