Hardy space on the upper plane

Question

Recently,I need to study something about Hardy space. However, many books only contain Hardy space on the unit disk. Is there any book having detailed description about Hardy space on the upper plane or on the plane $\mathscr{Re}\gt \frac{1}{2}$?

Any link or reference would be warmly welcomed!

Answer 1

Two good books covering Hardy spaces are the following:

1. Grafakos, Modern Fourier Analysis, 2009
2. Stein, Harmonic Analysis, 1993